identify the solution(s)of the system of equations, if any -2x-4y=1 and 12y=-6x-3

if you rearrange into the same format, you have

2x+4y = -1
6x+12y = -3

If you multiply the 1st by 3, you see that it is the same as the 2nd. So, they are really the same line, and there are infinitely many solutions.

That is, every point on the 1st line is also on the 2nd line -- they are the same line!