An atom of silicon has a mass number of 28 and an atomic number of 14. how can you determine how many protons and how many neutrons are in this atom?

The atomic number of an atom is the number of protons in its nucleus.
If the silicon atom has an atomic number of 14, then there are 14 protons
in its nucleus.

The mass number of the atom is the total number of (protons + neutrons)
in its nucleus.  If the silicon atom has a mass number of 28, and we know
that 14 of those are protons, then neutrons account for the other (28 - 14)
                                                                                       = 14 neutrons.

You may be wondering about all the electrons whizzing around the nucleus.
That's an excellent question, one that I thought you weren't going to ask. 

In a neutral atom, the number of electrons is the same as the number of
protons, so their number is the same as the atomic number. 

Regarding the atom's mass, the electrons make just about zero difference ...
one neutron or one proton has the mass of about 1840 electrons, so there's
practically no difference if we ignore the electrons completely.