Take log of all function with base 2
log(f(n)) = Log(2^n) = n
log(g(n)) = Log(n!) = Log(n^n) // using sterling approximation = nlogn
Log(h(n)) = Log(n ^ logn) = log(n) * log(n).
It becomes clear now that h(n) < f(n) < g(n).
Looking at options D is only option which satisfy this constraints.