Hello, Brent!

It's simple arithmetic . . .

6. A 2-by-4-by-8 rectangular solid is painted red.

It is cut into unit cubes and reassembled into a 4-by-4-by-4 cube.

If the entire surface of this cube is red,

how many painted unit-cube faces are hidden in the interior cube? Code:

8
* - - - - - - *
/ /|
4 / / | 2
/ / |
* - - - - - - * *
| | /
2 | | / 4
| |/
* - - - - - - *
8

The total surface area is:

. .

There are 112 red faces on the sixty-four unit cubes.

Code:

* - - - - *
/ /|
4/ / |
/ / | 4
* - - - - * |
| | *
4 | | /
| | /4
| |/
* - - - - *
4

The total surface area of the cube is: .

There are 96 red faces on the outside of the cube.

Therefore, there are: . red faces hidden inside.