Okie, so there are 2 ways to approach this problem. One way is to solve the problem via substitution. The other method which I'll use in this case is plug it in. So, let's go one by one.
2(0) - 2(-6) = 12 yup
2(4) - 2(-2) = 12 yup
2(-6) - 2(0) = 12 nope
2(-2) - 2(4) = 12 nope
So we canceled it down to 2 left. Now, plug the two possible answers into the second equation.
(-6) ^ 2 + (0) ^ 2 = 36 yup
(-2) ^ 2 + (4) ^ 2 = 36 nope
The answer that fits both equation is therefore the first one (-6,0)
I hope this helps :-)