We started with clue F. We know that A x B = A. Using our knowledge of multiplication, we deduced that the only number that A can be is 0. We concluded that the red triangle must be 0.
We then moved on to clue H. We found that A x B = B. The only multiple that would work in this equation is 1. This means that the yellow parallelogram must equal 1.
Clues D and C are both square numbers. We knew that there was only a range of 1-12 for these numbers. There are only 3 possible square numbers that it could be. However, 1 x 1 = 1, and this did not fit in with the equation, so we deduced that neither of the numbers could be 1. Clue D is very closely linked with clue B. However, if clue D was 3 squared, then 3 x 9 = 27, a number way over 12. This means that the pink square is 2, and the orange oval is 4. Therefore, the blue rectangle is 3, and the green 8 pointed star is 9.
We now have sufficient information to solve clues A, E, B and G. We know that 2 x 4 = 8, meaning that the the yello semi-circle is 8. Now for clue A. We know that 3 x 4 = 12. This means that the red circle is 12. Clue E says that ? x 2 = 12. Using division, we know that 12 / 2 = 6. The green triangle is 6. Finally, clue G. We know that the blue hexagon is 10 and the pink square is 2. Yhis means that the purple star must be 5.