As with most of Mendelian genetics problems, this is really a math
problem in disguise. Since most of us don't do combination problems
in real life, I prefer to look at these questions from a practical
(i.e., write it out) point of view.
First you need to remember that gametes only have one copy of an
allele, while regular cells have two. So, the gametes from our
genotype will have EITHER F or f, plus EITHER G or g, plus EITHER H or
h. Here are our options:
There are eight possible gametes. My math friends would have said
"duh" - pairwise combinations come in factors of 2. Since we have
three genes here, the possibilities are 2 cubed, or eight.