10776 ÷ 6 = 1796 R0
Alright, let's work through the division of 10776 by 6 step by step.

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

Step 2:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 10 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: 17
Subtract 42 from 47 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 4:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 179
Subtract 54 from 57 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 5:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 1796
Subtract 36 from 36 to get 0.

The final result is 1796 with a remainder of 0.