We divide 4321 by 6
We want to figure out the number of times 4321 can be divided by 6.

On to step 1:
The number 6 fits into 4 0 times, leaving a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 6

Let's proceed to step 2:
6 can be fit into 43 7 times, resulting in a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we take 42 away from 43, we end up with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 6

Moving on to step 3:
12 divided by 6 is 2 with a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 72.0
Deduct 12 from 12 and we're left with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 6

Going ahead to step 4:
1 divided by 6 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 720.0
The remainder is 1 after subtracting 0 from 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 5:
If we divide 10 by 6, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 720.1
Deduct 6 from 10 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 6:
6 can be fit into 40 6 times, resulting in a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 720.16
Subtract 36 from 40 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 7:
The number 6 fits into 40 6 times, leaving a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 720.166
Subtract 36 from 40 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 720.166 and a remainder of 0.0004.