need to know if there is an infinite solution, no solution or one solution to 2x=4x?

Think about it. Divide both sides by 2x and you get 1=2 originally 0=2. Oops.

Or if you want to look at it in another way;

2x = 4x

is derived from the simultaneous equations of:
y = 2x and
y = 4x

If you can visualise the graphs they make, do they meet?

If yes, then you'll find that there is a solution. In fact, the solution is at x = 0.

2x = 4x

0 = 4x - 2x
0 = 2x

Therefore, x = 0.

[EDIT: KISS

Dividing both sides by 2x give 1 = 2, not 0 = 2 ;)]