Here's what I think the prism looks like:

There are 3×3×2=18 cubes in the prism. The front and rear faces of the prism are the only ones having a central cube which will only have one painted face. All the remaining 16 cubes have at least two painted faces because they are positioned where at least two faces of the prism meet. The 8 corner cubes are positioned where three faces of the prism meet. Another 8 cubes are sandwiched between corner cubes and each has 2 exposed faces to be painted.
So the answer is: 16 cubes have at least 2 painted faces.