33567 ÷ 9 = 3729 R6
Alright, let's work through the division of 33567 by 9 step by step.

Step 1:
9 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 9

Step 2:
9 goes into 33 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 27 from 33 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 9

Step 3:
9 goes into 65 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 37
Subtract 63 from 65 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 9

Step 4:
9 goes into 26 2 times with a remainder of 8.
Write down 2 as next digit of of the result. 
Result so far: 372
Subtract 18 from 26 to get 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 9

Step 5:
9 goes into 87 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 3729
Subtract 81 from 87 to get 6.

The final result is 3729 with a remainder of 6.