83506 ÷ 6 = 13917 R4
Alright, let's work through the division of 83506 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 (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 2:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 23 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 6

Step 3:
6 goes into 55 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 139
Subtract 54 from 55 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 4:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1391
Subtract 6 from 10 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 5:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 13917
Subtract 42 from 46 to get 4.

The final result is 13917 with a remainder of 4.