Explanation of "Loan Repayment" Solution

One of the harder problems, according to USACO.guide, is Loan Repayment. I have looked over the official editorial and don’t fully understand what the solution encompasses. I would be grateful for any help or further explanation as to what to do and why it works. Thanks so much!

Here is the link to the problem: Loan Repayment Problem

Here is the link to the official solution: Loan Repayment Solution

Use some math to compute the max number of days numdays such that FJ gives Bessie the same amount of milk on each of those days.

Not sure what you mean. In the solution, you can see that FJ gives Bessie y gallons of milk for numdays.