Toilet supply line/tube sprays water from below the coupling nut

Knowing where the water lands gets you in the area, but what you really need to know is where the water came from. Is the tank cracked, is the supply line failing, is there a bad connection on either end of the supply line, or is the valve itself going.

If the tank is cracked, you'll have to buy a new one, and it's a large project if you're not used to working on basic plumbing jobs or are skirmish around an open toilet.

A bad supply line can be easily replaced and it's even easier if it's just the washers.

A bad valve may just have some dirt or buildup in it that will be fixed by opening and closing it once or twice with water running through it (an empty toilet tank). Though keep in mind any dirt may then get in the toilet valve and could cause it to run slowly until you clean it out. If that were to happen, just post another question. It could also be the packing material in the valve, which I've never touched on this type of valve. If that's the case, you may be able to minimize it by opening the valve all the way. If the valve is too far gone, you'll likely need a blow torch and solder to replace it. This can be a DIY job, but if you get in over your head, the water for the whole house will need to be shutoff until you can get a plumber out.

The washer under the nut is probably leaking and the easiest/best solution's would to be replace the pipe.

Why

The reason it only leaks when you have the supply on is that there is no significant back pressure on the fittings from the tank as the tank has an air gap and the filler is at the top of the tank not submerged at the bottom ( which would cause back pressure)

P.S. DON'T use mutigrips, use a spanner or shifting spanner, on a plastic nut (or even brass) you can deform the nut by the crushing force of the mutigrips as you tighten the nut.