8109 ÷ 6 = 1351 R3
We're going to perform division on 8109 with 6 as the divisor.

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 (0) of the dividend behind the 3 and repeat the process: 30 / 6

Step 3:
6 goes into 30 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 135
Subtract 30 from 30 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: 1351
Subtract 6 from 9 to get 3.

The final result is 1351 with a remainder of 3.