6609 ÷ 6 = 1101 R3
Alright, let's work through the division of 6609 by 6 step by step.

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

Step 2:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 6 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 3:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 110
Subtract 0 from 0 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 6

Step 4:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1101
Subtract 6 from 9 to get 3.

The final result is 1101 with a remainder of 3.