I don't understand this question at all.

If f(x) = 4x - 3 and h(x) = 4x^2 - 21, find a function g such that f ͦ g = h.

Ask yourself what function results in 4x^2 -21 when you multiply it by 4 and subtract 3 (the f(x) operation).

4 g(x) -3 = 4x^2 -21
4 g(x) = 4x^2 -18
g(x) = x^2 - 18/4

That is the answer