6756 ÷ 4 = 1689 R0
Let's divide 6756 by 4.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 4

Step 2:
4 goes into 27 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 27 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 3:
4 goes into 35 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 168
Subtract 32 from 35 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 4

Step 4:
4 goes into 36 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 1689
Subtract 36 from 36 to get 0.

The final result is 1689 with a remainder of 0.