rearranging the second equation, you get x = 2 + y, so we can substitute this into the first equation.
Its actually more useful to rearrange the second one into - y = 2 - x, or y = x - 2, so we dont have to use FOIL
Plugging this into the first equation, its x - 2 = 4 - x^2, adding 2 to both sides, x = 6 - x^2. At this point, we can just kinda bash it out, (bad strategy but in competition its easier to do this than actually go through each problem but hopefully somone else explains going the full route), but testing values, 2, is immediatly the answer. 2 = 6 - 4 which is true, so x = 2. Just looking at the other two answers, -4 doesnt work, but -3 does, -3 = 6 - 9, so the answer is D.
Again, this is a more competition style way to quickly observe the answer instead of hashing the full thing out, and instead just bashing it.