We get the above answer by noting that g(x) must be linear otherwise when applied to (x+4) we would not get another linear function.

So suppose g(x)=ax+b

g(f(x))=g(x+4)=a(x+4)+b=ax+4a+b

Now we are told that g(f(x))=4x-1

So

a=4 and 4a+b=-1

4(4)+b=-1

16+b=-1

b=-17

So our functiong g(x) must be

g(x) = 4x - 17

It is given that f(x) = x + 4 and h(x) = 4x - 1. We have to find g(x) such that g(f(x)) = h(x)

g(x + 4) = 4x - 1

(4*(x + 4) - 17) = 4x + 16 - 17 = 4x - 1

The function g(x) = 4x - 17

One function g(x) that gives g(f(x)) = h(x) is g(x) = 4x - 17