6778 ÷ 2 = 3389 R0
Alright, let's work through the division of 6778 by 2 step by step.

Step 1:
2 goes into 6 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 6 from 6 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 2

Step 2:
2 goes into 7 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 33
Subtract 6 from 7 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 2

Step 3:
2 goes into 17 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 338
Subtract 16 from 17 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 2

Step 4:
2 goes into 18 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 3389
Subtract 18 from 18 to get 0.

The final result is 3389 with a remainder of 0.