Answer: g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.
Step-by-step explanation: The expression g(x) - h(x) can be found by subtracting h(x) from g(x).
g(x) = -3x^2 + 2x - 6
h(x) = -4 - x
So,
g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.