If an atom has a mass number of 16 and atomic number of 8, how many protons, neutrons, and electrons does the atom have

First, we need to know what are a mass number and atomic mass. A mass number means the sum of protons and neutrons in an element (not electrons because they're too light), and atomic number is the number of protons only. 

So, when the atom has an atomic number of 8, it also means that the number of protons is 8. With that being said, we can find out the number of neutrons by subtracting 16 by 8, which makes 8. 

Electrons of an atom are always the same as protons. If the number of electrons is different to the number of protons, it should not be an atom, but an ion instead. So, we can deduce that the atom has 8 electrons.

So there is your answer, 8 protons, 8 neutrons, and 8 electrons.