76736 ÷ 6 = 12789 R2
Alright, let's work through the division of 76736 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 2:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 16 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 6

Step 3:
6 goes into 47 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 127
Subtract 42 from 47 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 4:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 1278
Subtract 48 from 53 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 5:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 12789
Subtract 54 from 56 to get 2.

The final result is 12789 with a remainder of 2.