If a 100.-g sample of platinum metal has a volume of 4.67 ml, what is the density of platinum in g/cm3?

The density of any substance does not change at a certain temperature and pressure. Even though mass and volume are intensive properties (depends on the amount of substance), density is not. It is merely a fixed ratio of mass to volume. Therefore, the solution is

Density = Mass/Volume
For your information, quantitatively, cm³ is equivalent to mL.
Density = 100 g/4.67 cm³ = 21.41 g/cm³