Question

A cube is colored red on all 6 faces. It is cut into 64 identical smaller cubes of equal size.Then how many cubes have two red opposite faces

Answer 1

I'm not sure what do you mean by 2 red opposite faces the answer could be 0 as the cubes with 2 red faces will have the paint on the adjacent faces. If you are trying to count them then:

The smaller cubes on the faces of the bigger cube will have just 1 red face, the cubes on the corners will have 3 red faces and the cubes only on the edges will have 2 red faces.

Since the cube is cut into 64 pieces, means along the edges there will be 4 squares.
${64}^{ \frac{1}{3} } = 4$
among these 4 two will be on the corners with three sides painted red and 2 will be on the edges with two sided painted red.
And there are 12 edges in the square. So the answer would be:
$12 \times 2 = 24$