86767 ÷ 6 = 14461 R1
Alright, let's work through the division of 86767 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 (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 3:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 144
Subtract 24 from 27 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 4:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 1446
Subtract 36 from 36 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 6

Step 5:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 14461
Subtract 6 from 7 to get 1.

The final result is 14461 with a remainder of 1.