2361 ÷ 6 = 393 R3
Alright, let's work through the division of 2361 by 6 step by step.

Step 1:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 2:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 18 from 23 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 3:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 39
Subtract 54 from 56 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 4:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 393
Subtract 18 from 21 to get 3.

The final result is 393 with a remainder of 3.