We look at the division of 3977 by 6 
Let's see how many times 6 fits into 3977.

Moving on to step 1:
6 goes into 3 0 times with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 6

On to step 2:
If we divide 39 by 6, we get 6 and a remainder of 3.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 3 after subtracting 36 from 39.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 6

On to step 3:
37 divided by 6 is 6 with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 66.0
If we subtract 36 from 37, we get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 6

Moving on to step 4:
6 can be fit into 17 2 times, resulting in a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 662.0
Deduct 12 from 17 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 5:
If we divide 50 by 6, we get 8 and a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 662.8
If we subtract 48 from 50, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 6:
20 divided by 6 is 3 with a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 662.83
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 662.833
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 662.833, and the remainder is 0.0002.