Red Triangle = 0
Yellow Diamond = 1
Pink Square = 2
Blue Rectangle = 3
Orange Oval = 4
Purple Star = 5
Green Triangle = 6
Yellow Semicircle = 8
Green Hexadecagon = 9
Blue Hexagon = 10
Red Circle = 12
I started by realising that the yellow diamond must be equal to 1 because of the equation in the box labelled H. I later realised that the blue hexagon could have been equal to 0 instead; however, I decided to continue anyways. From here I concluded that the red triangle must be equal to zero because the only alternative was 1 and that had already been taken. Next, after solving the equation in the box labelled D, I concluded that the pink square must be equal to 2, and therefore the orange oval must be equal to 4. This is because the orange oval is equal to the pink square^2. Because of this the orange oval must be equal to 1, 4 or 9 as they are the only square numbers under 12. I concluded that the orange oval must be equal to 4 and not 1 or 9 because 1 had already been taken and the orange oval is used in a later equation meaning that if it were equal to 9, then the answer would be greater than 12 because the other shape involved was not the yellow diamond. I then used the numbers that I already had to solve the remaining equations giving me the answers above. After checking I was able to conclude that my answers were correct.