A block 4 cubes long, 3 deep and 2 high is built from small cubes. How many of the small cubes are in contact with exactly three others?

Every cube touches one cube above or below it. A corner of a layer touches 2 cubes in its layer, 3 in all; edge cubes touch 3 in the layer (4 in all) and inner cubes 4 (5 in all). Each layer has 4 corners, so $2\times 4=8$. (12 counts the edge cubes, which touch four.)