What is the gfc of h^4 and h^8

We can write h^8 as h^(4+4) = h^4*h^4. So buried inside h^8 are two copies of h^4 multiplied together

So both terms have a greatest common factor of h^4

If you had something like h^4 + h^8, then it would factor to h^4(1 + h^4)