Likely to be a question set by a non-native speaker, applying rules but not thinking about meaning. The best response is D.
A. is grammatically correct, and it answers the question. But the answer doesn't make sense. "Day off" implies you don't have work.
B. Is grammatically well formed, but doesn't answer the question. The question asks for usually, the answer concerns one particular future event.
C. Is not grammatically correct, as it is missing a verb "I usually do not do much" would be ok.
D. Is the best response. It means "I usually do nothing much, because I always sleep until noon".
So a simple badly made question, or an error on the part of the test setter. Don't worry about it.
@user178049 is correct in that "[distinguish] the good from the bad" is an expression. Though you could fit other verbs in there besides just "distinguish." For example, you can take the good and take the bad, and then you've got the theme song for an American sitcom from the '80s.
The point is really that taking out the articles changes the meaning a bit (or at least makes the meaning a bit more ambiguous).
One must learn to distinguish good from bad
is a perfectly acceptable English sentence. But that's not super hard for most people. Little kids generally understand the difference between good and bad, or right and wrong. The trick is applying the theory to the real world.
In the real world, you've got gray areas. You've also got things or people or ideas that might seem good or bad on the surface but are actually the opposite.
That's why we add in the articles. "The good" and "the bad" refer to the specific things in the world that are good and not bad, or vice versa – whatever those things may be. (So they're "specific," but only sort of.)
In answer to your other question about "distinguish," I would say it is okay here. That is just a simple infinitive. You could say "how to distinguish," though; that's okay too.
To me,
One must learn how to distinguish good from bad
implies maybe a slightly different emphasis than
One must learn to distinguish the good from the bad
But I'd say they both get at approximately the same idea.
Best Answer
Each one of you makes it clear that you are directly addressing a group of people. When directly addressing people, the possessive to use is your. Unless, that is, each person is being tasked with convincing a male third party of something, in which case his can be used. This context must already have been established for this usage though.
If you are not directly addressing people, but are instead reporting about a group of people, then you would not use you and your, you would instead use them and their or say "Each one must make up their mind" (without the them).
I would tend to steer clear of his/her in this situation unless it is made clear at the start of the sentence that the group is all male or all female, and even then I might still use their.