The top of this cube is red, its front blue and its right side green; the three hidden faces are not painted. After cutting along the lines, how many small cubes show exactly two colours?

Two colours appear on the three edges where two painted faces meet: top–front, top–right and front–right. Each of those edges has 5 cubes, but the corner cube where all three meet shows three colours. So $3\times 4=12$. (15 includes that corner three times.)