9516 ÷ 6 = 1586 R0
No problem, we've got 9516 and 6 for the division.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 35 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 3:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 158
Subtract 48 from 51 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 4:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 1586
Subtract 36 from 36 to get 0.

The final result is 1586 with a remainder of 0.