159634

Firstly, I thought of a whole number that is a multiple of both 3 and 4. Twelve was the first number I thought of. This however, did not work because it only worked for quarters and not thirds. Then, I thought of another number that was divisible by 3 and 4. I thought of 24. This did work because a quarter of 24 is 6 and a third of 24 is 8, and the difference between six and eight is two. Which is the amount of coins I had to turn over!