The trick here is to realize that you're actually looking for the number of orbitals that are present on the third energy level in a given atom.
This is the case because, as you know, each orbital can hold a maximum of
Since you're only looking for the number of electrons that have spin-up, you need to take the total number of electrons present per orbital and divide it by
As you know, the total number of orbitals present on an energy level described by a principal quantum number
#color(blue)(ul(color(black)("no. of orbitals" = n^2)))#
In your case, you have
#n = 3#
which means that the third energy level can hold a maximum of
#"no. of orbitals" = 3^2#
#"no. of orbitals" = 9#
Since each orbital can hold a single electron that has
#n = 3, m_s = +1/2#
in a given atom.