Oxygen is denoted as 16o *. how many protons and neutrons does an oxygen atom have?

The 16 refers to the atomic mass, the total number of protons and neutrons in the nucleus.

We know Oxygen has atomic number of 8, this can be seen by looking at a periodic table. 

This means Oxygen must have 8 protons in the nucleus.

As:
 
Neutrons + Protons = 16,

And the number of protons = 8,

Neutrons + 8 = 16

Neutrons = 8

There are 8 Neutrons in the nucleus.