66644 ÷ 9 = 7404 R8
Alright, let's work through the division of 66644 by 9 step by step.

Step 1:
9 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 2:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 63 from 66 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 9

Step 3:
9 goes into 36 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 74
Subtract 36 from 36 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 9

Step 4:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 740
Subtract 0 from 4 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 9

Step 5:
9 goes into 44 4 times with a remainder of 8.
Write down 4 as next digit of of the result. 
Result so far: 7404
Subtract 36 from 44 to get 8.

The final result is 7404 with a remainder of 8.