12. (3 points) A large rectangular block of wood is painted red on all its surfaces, then divided into several equally sized smaller rectangular blocks. Among these, the number of smaller blocks that have exactly two red faces is exactly 12. What is the minimum number of smaller rectangular blocks into which the large rectangular block must be divided?
【Answer】Solution: Since the small rectangular prisms with only two red faces are located on the edges (excluding the endpoints of the edges); to minimize the number of blocks, 8 of the 12 edges can have only the two small rectangular prisms at the endpoints, and the middle of the other 4 edges can have: $12 \div 4=3$ (pieces), the total number of small rectangular prisms divided: $(3+2) \times 2 \times 2=20$ (pieces). Therefore, the answer is: 20.