6142 ÷ 6 = 1023 R4
Let's divide 6142 by 6.

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

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 6

Step 3:
6 goes into 14 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 12 from 14 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 4:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 1023
Subtract 18 from 22 to get 4.

The final result is 1023 with a remainder of 4.