19268 ÷ 6 = 3211 R2
Alright, let's work through the division of 19268 by 6 step by step.

Step 1:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 2:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 18 from 19 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 6

Step 3:
6 goes into 12 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 32
Subtract 12 from 12 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 6

Step 4:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 321
Subtract 6 from 6 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 6

Step 5:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 3211
Subtract 6 from 8 to get 2.

The final result is 3211 with a remainder of 2.