Area=length×breadth, 42.56=6.4×breadth, breadth=42.56/6.4=6.65cm.
Here are two ways to do the calculation.
(1) 6.4=8×0.8 so we can divide by 8 first: 42.56/8=5.32, then we have to work out 5.32/0.8 which is the same as 53.2/8, which gets rid of the decimal point in the divisor. 53.2/8=6.65(cm). This method does not require long division as long as you know how to divide by 8.
(2) Long division:
6.4)42.56 is the same as 425.6 divided by 64 (the decimal point has been shifted one place to the right in the dividend and the divisor so we don't have to worry about a decimal point in the divisor).
64)425.6 is now explained in detail. How many times does 64 go into 425.6? 6 goes into 42 7 times so let's try 7×64=448, which is too big, so we need 6×64=384. Subtract 384 from 425=41. We can also insert the decimal point in the quotient following 6:
6.
64)425.6
384
41
Now move on to the next digit, so we bring down the 6 to make 416. Note that the decimal point in the dividend can now be ignored since we've already discovered where the decimal point goes in the quotient. We know that 6×64=384 so we need to use this, because it's the closest multiple to 416. 416-384=32.
6.6
64)425.6
384
416
384
32
We would then bring down the next digit in the dividend, but there isn't one. However, we're beyond the decimal point so all digits following 425.6 are automatically zeroes. So the next digit to bring down is zero, making 32 into 320. How many times does 64 go into 320? Well, 6 goes into 32 about 5 times so let's try 5×64=320. That's exactly what we want! So the final digit in the divisor is 5:
6.65
64)425.6
384
416
384
320
320
0
That completes the division so the answer is 6.65 and we know we're working in centimetres so the breadth is 6.65cm.
Now here's a hint which tells you where to expect the decimal point in the division 42.56/6.4. Remove everything after the decimal points so we have 42/6=7, which is an estimate of the quotient and is very useful in determining where the decimal point is going to be. Since 7 is a single digit, the decimal point is going to go after the first digit of the quotient (which happens to be 6). Also, 7 is approximately the same size as 6.65, which makes us feel confident that we have the right answer.
See aslo https://www.mathhomeworkanswers.org/229159/find-the-breadth-of-a-rectangle-with-area-42-56-and-length-6-4?show=229161#a229161 for yet another method for finding the solution without using long division.