Counterexample to demonstrate there are no functional dependencies
To find if the functional dependency AB→G is implied by F you should find the closure of the attributes AB under F, i.e. AB+.

These are the steps:

AB+ = AB
      ABC     (using AB→C)
      ABCD    (using B→D)
      ABCDE   (using CD→E)
      ABCDEGH (using CE→GH)


and since G belongs to AB+, then AB→G can be derived from F.