4199 ÷ 6 = 699 R5
Alright, let's work through the division of 4199 by 6 step by step.

Step 1:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 2:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 41 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 3:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 69
Subtract 54 from 59 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 4:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 699
Subtract 54 from 59 to get 5.

The final result is 699 with a remainder of 5.