8269 ÷ 6 = 1378 R1
Let's divide 8269 by 6.

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 (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 2:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 22 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 3:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 137
Subtract 42 from 46 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 4:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 1378
Subtract 48 from 49 to get 1.

The final result is 1378 with a remainder of 1.