81568 ÷ 6 = 13594 R4
Alright, let's work through the division of 81568 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 2:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 21 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 3:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 135
Subtract 30 from 35 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 4:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 1359
Subtract 54 from 56 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 6

Step 5:
6 goes into 28 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 13594
Subtract 24 from 28 to get 4.

The final result is 13594 with a remainder of 4.