An shell contains 3s, 3d, and 3p subshells. Any s shell can hold up to two electrons, any p shell can hold six electrons, and any d shell can hold ten electrons.

This question is best solved by using quantum numbers. We are given the principle quantum number. Using this, we can work down to determine how many electrons can fit in this shell. The rules for quantum numbers are given below.

If the principle quantum number is three, then the next quantum number can be zero, one, or two. These correspond to the s, p, and d subshells, respectively.

After that, the next quantum number describes the orbitals within the subshells. Each orbital can carry two electrons, according to the final quantum number.

In total, there are eighteen electrons allowed in all subshells of the third energy level.