96638 ÷ 6 = 16106 R2
Alright, let's work through the division of 96638 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 (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 4:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 1610
Subtract 0 from 3 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 5:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16106
Subtract 36 from 38 to get 2.

The final result is 16106 with a remainder of 2.