8634 ÷ 6 = 1439 R0
Alright, let's work through the division of 8634 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 (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 2:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 26 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 3:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 143
Subtract 18 from 23 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 6

Step 4:
6 goes into 54 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 1439
Subtract 54 from 54 to get 0.

The final result is 1439 with a remainder of 0.