The question essentially wants you to find half of the maximum number of electrons that can reside on the third energy level, i.e. the number of orbitals present on this energy level.
As you know, the spin quantum number,
#m_s = +1/2 ->#the electron has spin-up
#m_2 = -1/2 ->#the electron ahs spin-down
According to Pauli's Exclusion Principle, each individual orbital can hold a maximum of two electrons, one having spin-up and the other spin-down.
This implies that in order to find the total number of electrons that can have
Now, the total number of electrons that can reside in a given energy level is equal to
#"total no. of electrons" = 2n^2#
In your case, you have
#"total no. of electrons" = 2 * 3^2 = 18#
This means that the number of electrons that can have
#"18 e"^(-)/2 = "9 e"^(-)#
In other words, the third energy level can hold