51374 ÷ 6 = 8562 R2
Alright, let's work through the division of 51374 by 6 step by step.

Step 1:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 2:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 48 from 51 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 3:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 85
Subtract 30 from 33 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 4:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 856
Subtract 36 from 37 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 6

Step 5:
6 goes into 14 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 8562
Subtract 12 from 14 to get 2.

The final result is 8562 with a remainder of 2.