for 337-25+48=360 (without the new value of 2nd shelf)

The reason why is divided by 9 unit it is because you do not know how much is been added to the 2nd shelf. But you know that the original book value is 4 times the book after it is been added.

So it is deduced that both new value of shelf 1 and 3 are 4 units each. And thus u will get 9 units (8 units[ new 1 and 3 shelf ] + 1unit [old value of shelf 2]).

337 is the shaded part at the beginning.
Draw your model so that at the end of the day, they will all have equal length.
Hence first step is to remove 25 first the first shelf,
next, add 3 more units to 2nd
lastly is to add 48 to the third shelf
Then you will be able to see 9 units: 4 units from 1st shelf, 1 unit from 2nd and another 4 units from 3rd.
Thus, use 360 divide by 9 to find 1 unit.
Since 3rd shelf is 4 unit, you multiply by 4 and minus away 48 since the question want at first.