Only two faces of this cube are painted, the top yellow and the front blue. After cutting along the lines, how many small cubes have exactly one painted face?

Each painted face has 16 squares, and the 4 cubes along the edge where the top meets the front are painted on both. So each face has $16-4=12$ cubes painted only there: $2\times 12=24$. (32 counts the shared edge twice.)