96684 ÷ 6 = 16114 R0
Alright, let's work through the division of 96684 by 6 step by step.

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 (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 2:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 36 from 36 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 6

Step 3:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 161
Subtract 6 from 6 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 6

Step 4:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1611
Subtract 6 from 8 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 6

Step 5:
6 goes into 24 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 16114
Subtract 24 from 24 to get 0.

The final result is 16114 with a remainder of 0.