32762 ÷ 6 = 5460 R2
Alright, let's work through the division of 32762 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 (2) of the dividend behind the 3 and repeat the process: 32 / 6

Step 2:
6 goes into 32 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 32 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 3:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 54
Subtract 24 from 27 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 4:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 546
Subtract 36 from 36 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 5:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 5460
Subtract 0 from 2 to get 2.

The final result is 5460 with a remainder of 2.