6478 ÷ 6 = 1079 R4
No problem, we've got 6478 and 6 for the division.

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 (4) of the dividend behind the 0 and repeat the process: 4 / 6

Step 2:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 4 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: 107
Subtract 42 from 47 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 4:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 1079
Subtract 54 from 58 to get 4.

The final result is 1079 with a remainder of 4.