Explanation:
If the equation were to not have infinitely many solutions, we would be able to solve the equation to find the finite solution(s). So it might be useful to see if we can solve for x first off.
So we have:
-2(3x+6)=-6(x+2)
First try simplifying this a bit by multiplying out both sides:
-6x-12=-6x-12
Add 12 and this simplifies even further to:
-6x=-6x
Divide by -6 and it simplifies yet again to:
x=x
We cannot simplify this equation any more without getting rid of x entirely. The rest of the terms in this equation cancel eachother out; they do not effect x nor does x effect them. x could be any value and it wouldn't stop the other terms from cancelling eacother out. Therefore the possible range of values for x is infinite.