Base on the given question i can deduce than f(n)<{g(n)=h(n)}
lets take an instance of three and solve the question :
let f(n)=logn,g(n)=n,h(n)=n;
1. f(n)+h(n)=theta(g(n)) ==> n+logn = n ? correct SO TRUE
2. f(n)*h(n)=theta(g(n)*h(n)) ==> n*logn = n*n ? nopes nlogn != n2 SO FALSE
3. g(n)*f(n)=big omega(h(n)*f(n) ==> n*logn <= n*logn ? correct make c=2 ! SO TRUE
4. h(n)+g(n) = O(f(n)) ==> n+n <= logn ? nopes it should be small omega! SO False