6747 ÷ 6 = 1124 R3
Alright, let's work through the division of 6747 by 6 step by step.

Step 1:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 6 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 6

Step 2:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 7 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 6

Step 3:
6 goes into 14 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 112
Subtract 12 from 14 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 4:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 1124
Subtract 24 from 27 to get 3.

The final result is 1124 with a remainder of 3.