How many atomic orbitals are there in an f subshell?

3 right? I always get confused with the silly notation.

In an atom, what is the maximum number of electrons that can have a principal quantum number n = 4?

I never really understood this principle now i thought that the answer would be 32 because for each magnetic quantum # there are 2 electrons, but that didn't work out so well. So then I thought I would divide by 2, and make my answer 16 - because the electrons are all spinning in different directions.

Well as you can tell from reacing this - I am VERY lost!

any hints or nudges in the right direction would be AWESOME!!