This one is probably a softball question, but...
Fact: A cube has 6 faces
Fact (unless my math is wrong): A cube that is cut in half center horizontal can be reoriented to have 18 unique faces. (The top and bottom stay the same. The other four sides have 16 combinations: A/A, B/B, C/C, D/D, A/B, A/C, A/D, B/A, B/C, B/D, C/A, C/B, C/D, D/A, D/B, D/C)
Question: How many faces could the cube have if it is cut center horizontal and center vertical?
Constraint: You cannot "lift a piece" out of the cube and reorient it. The entire cube must be rotated, like a Rubik Cube.
Correction: It would have to be cut center vertical along the front and the side. Otherwise it doesn't rotate properly! So in otherwords, it is a 2x2 Rubik Cube instead of a 3x3 Rubik Cube.