86559 ÷ 9 = 9617 R6
Alright, let's work through the division of 86559 by 9 step by step.

Step 1:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 8 to get 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 9

Step 2:
9 goes into 86 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 81 from 86 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Step 3:
9 goes into 55 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 96
Subtract 54 from 55 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 4:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 961
Subtract 9 from 15 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 9

Step 5:
9 goes into 69 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 9617
Subtract 63 from 69 to get 6.

The final result is 9617 with a remainder of 6.