The number is the ASIN: Amazon Standard Identification Number.
For books often the same as the ISBN, but Amazon makes their own for e.g. self-published books through Amazon/Audible (same company).
Anyway, the ASIN is the vital part of the link that identifies exactly which book, recording, etc.
Also: Please do not provide a search link. Often that gives a page of results, that will change with time, and may include many other books than the one you intend. Do the search and then go to each result and get its link.
Sometimes a "series" link is useful though, as that lists only the books in that series.
E.g. for the above, the series link for "King's Dark Tidings" is
https://www.audible.com/series?asin=B01LR5WDEC&ref=a_pd_Sci-Fi_c1_series_1&pf_rd_p=4df5109d-f867-4b0f-81d9-bbb0a0713d9e&pf_rd_r=7GDJ3JMFD553PFAGGAVM&But again, trim that after the ASIN to
https://www.audible.com/series?asin=B01LR5WDECand you will see that works precisely.
The part after the ASIN is a reference to the page you came from and when you made the search. For the more paranoid, it could tell Amazon your customer ID. Though I think the risk of any blowback is close to zero.
Anyway, when I review requests I usually trim the link, which is why you might see the little "Last Edit" notation. But of course it would be cleaner and less hassle all around if requesters could do that themselves. Makes it more obvious if links are dupes, for instance, if they only have different refs.