Using the three positions of the die, find the sum of the numbers on the faces opposite 1, 2 and 3.

1 is seen with 2, 3, 6 and 4, so 1 is opposite 5. 2 is seen with 1, 3, 5 and 4, so 2 is opposite 6. That leaves 3 opposite 4. Opposite 1, 2 and 3 are 5, 6 and 4: $5+6+4=15$. (6 adds 1, 2 and 3 themselves; 21 adds all six faces.)