For this question is the answer = 24 (option C)?

Approach:

Not possible. If we look only at the first condition (i.e, fixing G as the third letter), there are 4! = 24 ways. The second condition means that the total number of rearrangements possible must be less than 24.

One mistake with your approach is that you’re actually allowing repeats (for instance, there is nothing stopping K and K being the first two letters if we use your method).

You are correct.

So this time I took the approach of finding total arrangements and subtracted the cases where G & H are together

Is this correct? - @Leaderboard

That looks correct.