I presume you meant:
1. (F → G) V H
2. ~G
3. ~H | ~F
You need to number your statements and g is not the same thing as G.
1. (F → G) V H
2. ~G
3. ~H | ~F
4. F → G 1,3 Disjunction Syllogism
5. ⸫ ~F 2,4 Modus Tollens
John

My calculator said it, I believe it, that settles it
From
I > Ø