To solve this problem, we first need to convert the mixed number 8 15/6 to an improper fraction.

8 15/6 = (8 * 6 + 15) / 6
8 15/6 = 48 + 15 / 6
8 15/6 = 63 / 6

Now, we can subtract the fraction 63/6 - 3 5/6.

63/6 - 3 5/6 = 63/6 - (3 * 6 + 5) / 6
63/6 = 63 - 18 - 5 / 6
63/6 = 40 / 6

Now, we can simplify the resulting fraction:

40 / 6 = 20 / 3

Therefore, the solution to 8 15/6 - 3 5/6 is 20/3 or 6 2/3.