44211 ÷ 6 = 7368 R3
Alright, let's work through the division of 44211 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 (4) of the dividend behind the 4 and repeat the process: 44 / 6

Step 2:
6 goes into 44 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 42 from 44 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 3:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 73
Subtract 18 from 22 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 4:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 736
Subtract 36 from 41 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 5:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 7368
Subtract 48 from 51 to get 3.

The final result is 7368 with a remainder of 3.