39663 ÷ 6 = 6610 R3
Alright, let's work through the division of 39663 by 6 step by step.

Step 1:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 2:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 39 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 3:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 66
Subtract 36 from 36 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 6

Step 4:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 661
Subtract 6 from 6 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 5:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 6610
Subtract 0 from 3 to get 3.

The final result is 6610 with a remainder of 3.