Both f(g(x)) and g(f(x)) are equal to simply x. This is because these two equations are inverse equations.
To find each of these composites, take the original equation and plug the other in for the x term. For f(g(x)) we start with the f(x) equation and then put g(x) in for x.
f(x) = -4x + 60 ----> Plug g(x) in for x
f(g(x)) = -4(-1/4x + 15) + 60 ----> Distribute the -4
f(g(x)) = x - 60 + 60 -----> Simplify
f(g(x)) = x
Then we can check the other in the opposite order.
g(x) = -1/4x + 15-----> Plug in f(x) for x
g(f(x)) = -1/4(-4x + 60) + 15 -----Distribute the -1/4
g(f(x)) = x - 15 + 15 ----> Simplify
g(f(x)) = x
And if both are equal to x, this means they are inverse functions.