I have a problem that reads as:

-4x-2y=12
4x+8y=-24
And when solved the answer is (2,-2), but I checked the answer in the back and it says (6,-6)
How does that WORK??

if you add the two equations, the x's cancel out, and you have

6y = -12
y = -2
so, x=2.

The book answer is wrong.

(6,-6) fits the 2nd equation, but not the 1st.

If the 1st equation were -4x-2y = -12
then (6,-6) would be correct.

So, it appears that the problem has a typo.