A solid cube of side 8 cm is painted red, blue and black on its opposite faces. It is cut into equal cubes of side 2 cm. What is the number of cubes painted on only two faces?

Given: 

We have a solid cube of side 8 cm that is painted on opposite faces with red, blue, and black and then cut into smaller cubes of side 2 cm.

Since the large cube has a side of 8 cm, and it is cut into small cubes of 2 cm, the number of cubes along each edge is:

​$$\frac {8}{2}$$ = 4​

So, the large cube is divided into 4 × 4 × 4 = 64 smaller cubes.

Cubes on the edges of the large cube but not at the corners are painted on exactly two faces.

Each edge of the large cube contains 4 small cubes.

The corner cubes are painted on three faces, so we must exclude them.

Excluding the two corner cubes from each edge, the remaining cubes on each edge are 2.

A cube has 12 edges.

Each edge has 2 cubes that are painted on exactly two faces.

So, the total number of such cubes is:

12 × 2 = 24

Number of cubes painted on only two faces = 24

Thus, correct option is (d).