3732 ÷ 9 = 414 R6
Alright, let's work through the division of 3732 by 9 step by step.

Step 1:
9 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 (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 2:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 37 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 9

Step 3:
9 goes into 13 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 41
Subtract 9 from 13 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 9

Step 4:
9 goes into 42 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 414
Subtract 36 from 42 to get 6.

The final result is 414 with a remainder of 6.