What is the number of electrons in a completely filled second shell of an atom? (1) 32 (2) 2 (3) 18 (4) 8

The second shell can only hold 2 electrons. 

Final 2 electrons

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n^2) electrons.

final (4) 8 electrons

The problem here is that according to aufbau principle before 3d orbital 4s subshell comes.after filling 3p orbital with electrons you have 4 electrons left, you place two in 4s with opposite spin and the other two in 3d in any of its two orbitals of total five orbitals with the same spin.