Let us see through counter examples :
For A) :
Let f(n) = 2n , g(n) = n and h(n) = 2n..So
f(n) is O(g(n)) is fine..But
h(f(n)) = h(2n) = 22n and
h(g(n)) = h(n) = 2n
So 22n is not O(2n)..
Hence A) option is false..
For B) :
f(n) != O(g(n)) meaning that f(n) > g(n) and hence g(n) < f(n)..So strict inequality exists..So g(n) = o(f(n)) not O(f(n)) as for O(f(n)) the tight upper bound need also be considered.
.Hence option B) is also false.
Hence D) is the correct answer ..