Why is it incorrect?
If you meant "reflect it with respect to the x-axis" then
y = x^2 - 4 is translated to -y = x^2 - 4
so then you have y = -x^2 + 4
moving it up 8 units is a vertical translation of 8, so y = -x^2 + 12. (which is what you have but not simplified)
If it was meant to be read reflection about the y-axis, then x -> -x, so that y = x^2 - 4. add 8 makes it y = x^2 + 4