The Challenge Rating of a monster is a very useful guide for judging the difficulty of an encounter, but it is not an exact science. Experience with your own players will tell you how tough an encounter they can handle, and what kinds of encounters they are best at.
When the entire party can gang up on a single monster (even one with multiple attacks) tactics on the battlefield can be less important than when they are outnumbered. However, the more monsters you have, the less certain the estimate of Encounter Level (EL) / "CR Equivalency" becomes. You should also be careful when advancing monsters (adding extra hit dice to increase their CR), as this too can lead to some nasty surprises.
I find this online calculator to be very useful for estimating EL, especially when I'm using monsters with a range of different CR's in a single encounter:
http://www.d20srd.org/extras/d20encountercalculator/
As far as multiple encounters per day are concerned, this too depends on a number of things. A fighter or a warlock can likely go for longer than a wizard, but even they likely have limited use magic items (particularly healing potions) that they will run out of eventually. When they are near a settlement where they can go shopping and are likely to get an uninterrupted 8 hours of rest, it isn't a problem. However, when they're deep in the Underdark, surrounded by enemies, things can get a bit tough.
Rather than having multiple EL 4 encounters in a row, you should aim for variety. Table 3-2 Encounter Difficulty, in the 3.5 edition DMG, recommends the following:
10% easy (EL lower than party level)
20% "easy if handled properly" (whatever that means...)
50% challenging (EL equals Average Party Level)
15% very difficult (EL 1-4 higher)
5% overwhelming (EL 5+ higher)
In Pathfinder, the range of encounters is a little tighter:
Easy (APL –1)
Average (=APL)
Challenging (APL +1)
Hard (APL +2)
Epic (APL +3)
(APL = Average Party Level)
However, I think that the advice still holds: don't aim to make every enounter "average". Now and then, throw something "epic" at them to keep 'em from getting too cocky. You should drop some pretty heavy hints, though, that they need to run away to avoid a TPK (especially the first time you do it). In a level-based game like D&D, it's always good to have something to strive for.
First off, all of edgerunner's answers are great. But I wanted to add some Dungeon World specifics:
Check p.19 and you'll see that 6- isn't "failure" - it's "trouble". The GM will say what happens and the player will mark XP. You are attaching non-DW simulationist ideas to DW mechanics by your supposition that 6- means "failure."
These principles can apply in all sorts of games, and have been used by GMs for years. If the PCs have to climb a fence, they're just going to keep trying until they succeed, right? So even in traditional games, many GMs will read "failed" rolls as a lack of some quality - not fast enough, not quietly enough, not without hurting themselves, etc., instead of just keeping them on the wrong side of the fence.
This is because failure is boring and stops moving the story forward. So you are correct, there is no plain-old failure in DW. It's not in the GM's agenda to make the PCs fail. There is no move for failure.
So the problem isn't that edgerunner's ideas are non-optimal, it's that your concept of what 6- means is wrong and that static failure doesn't exist in Dungeon World.
Expanding on 6-
From the text:
Generally when the players are just looking at you to find out what happens you make a soft move, otherwise you make a hard move.
Somewhere in Apocalypse World itself it says about hard moves:
make as hard and direct a move as you like
Early PbtA games like DW assumed you understood Apocalypse World. And this phrase is often tacitly implied in PbtA games even today.
6- means trouble as I said. The GM is free, on 6-, to make a move as hard as they like. That doesn't mean as hard as you can think of.
AW says:
It’s not the meaner the better, although mean is often good. Best is: make it irrevocable.
So while a 7-9 should substantially give the character what they wanted (they accomplish their intent even if their action created complication), on 6- you are free to deny the intent (the action still has to have consequences beyond "no" though) and in addition make a move as hard and direct and irrevocable as you like.
Climbing a mountain a soft move is "The boulders above you on the rock face begin to wobble as the grappling hook you've tossed up there sets itself. What do you do?"
A harder move is "The boulders have tumbled off the edge of the ledge and after hanging nearly motionless for a tiny instant above you, are now plummeting towards you, gaining speed every moment. What do you do?"
A really hard move is "The boulders are yanked free by your grappling hook and come smashing into you, tearing you from your narrow perch and scattering the contents of your pack into the yawning emptiness beneath. What do you do?"
Best Answer
As many as you think is reasonable.
The rules for Roll for Shoes don't specify how many dice the GM should roll, so it's left up to their discretion. Obviously, you can come up with any kind of more or less elaborate schemes for determining an appropriate number, but at least in the games I've run, the following simple scheme has worked quite well:
For ordinary tasks, roll one die. Everybody in RfS has the skill "Do anything (1)". This means that a one-die challenge is something anybody should have at least a 50% chance of succeeding in (but also something that most people should have a reasonable chance of failing; see below).
For challenging tasks, roll two dice. Anybody can still beat a two-die challenge, but the odds are against them. Even skilled characters have a fair chance of failing. Success is always awesome.
For heroic tasks, roll three dice. A random person will be almost sure to fail a three-die challenge, and it's risky for pretty much anybody. At least in my short games, level 4 skills are fairly rare (and pretty narrow in scope), so nobody really finds three-die challenges easy.
For nearly impossible tasks, roll four (or more) dice. IME, these kinds of challenges tend to happen only when players randomly attempt something they really should not be able to do, like jumping over buildings in a non-superhero game. You may sometimes want to just outright refuse such attempts, especially if someone tries to use them for XP farming. (I've never had that happen, but in principle, a sufficiently munchkinly player could try it.) Use your judgment, and see last paragraph below.
And finally:
For trivial tasks, don't roll. If a player wants to, say, open an ordinary unlocked door, that doesn't call for a roll. They just do it.
...that is, unless they really want to roll for it. A key feature of Roll for Shoes is that players can roll for anything — like, say, seeing whether they have shoes on.
Such situations are usually best treated as the player attempting to overdo the action, hoping for some impressive extra result, while also taking the risk of comically failing a task that should be trivial. So think of something awesome that should happen if the player succeeds really well ("You slam the door open, and knock over a goblin lurking just behind it, who hits another goblin behind him and knocks him over, too."), and something ridiculous that should happen if they fail ("The door comes off the hinges and hits you on the head."), and then roll one die.
Also, don't be afraid to improvise new mechanics if you think the situation calls for them. For example, for the final challenge in my last game, which involved competition between teams, I had the players describe how they would contribute to the team effort (and how they built on each other's contributions) using their specific skills, and then had them roll one die per player, plus one for each skill they managed to apply to the task; those dice were then pooled and compared to an arbitrary dice pool I rolled as the GM to represent the competing teams. It was completely ad hoc, but also a really awesome ending to the game.
Of course, these are all just my personal guidelines, suited for the way I run the game; one of the nice things about microsystems like RFS is that they're more of a starting point than a complete ruleset, so every GM and every group can develop their own way of doing things. Also, even for me, this is the first time I've even tried to describe the ad hoc way I choose challenge difficulties in any kind of systematic way; the real method I use is pretty much summarized in the headline at the top of this answer.
Also, I suspect a lot of this depends on the type of games you run, as well as on your players. I typically run short games that rarely end up involving combat or recurring enemies, so I've never felt a need to explicitly stat up (i.e. select skills for) NPCs. I've also noticed that my players frequently forget to mark or use XP, even if I remind them about it, which probably slows down skill gain somewhat. I'm also fairly strict about the rule that new skills must be narrower in scope than the one that was used to gain them, so even if players do end up gaining high-level skills, they're not very often applicable (at least not without either clever planning by players or fancy footwork by the GM).
Finally, there's one major practical exception to the "players can roll for anything" rule: don't allow a roll if you can't deal with the consequences. Of course, the whole point of Roll for Shoes is that you should let the story unfold as it will, and accepting the consequences of even unlikely rolls is part of that. But sometimes you may end up in a situation where you genuinely realize that letting a player succeed (or fail) at something would put you in a situation where you see no way to continue the game, and it wouldn't be right to just end the game there and then, either. If that happens, you may want to just openly admit it, and ask the player to please try something else.