I have always had trouble with circle permutations myself. Normally we would simply use (n-1)!. However, since this is a circular wire that can move around in space, you over count the permutations by 2. For problems like this, the required formula is (n-1)!/2. If you want an even better understanding, I would suggest researching the origins of the formula. With this formula, you can divide your 24 by 2 and get 12.