The volume of an octagonal prism is 486 cubic millimeters. If the area of the base is 54 square millimeters, what is the height of the prism?

prisms are simply a single 2D shape stretched out into 3 dimensions. Hence the volume of any prism is:

Volume of Prism = Area of Base * Height

Rearranging we find that:

Height = Volume of Prism / Area of Base

This is all you need. (assuming that the "base" referred to in the question is the octagon, which it should be)