First you must authorize your ADE with a specific Adobe ID.
(Help/Authorize Computer on the latest version, Library/Authorize Computer on the earlier more reliable v1.7.2)
If you have not already done that before borrowing the book,
return the book first, then register your Adobe ID, the then reborrow the book.
Then you must authorize the Kobo with the same ID.
(Help/Authorize Device on the latest version, Library/Authorize Device on v1.7.2)
Even if you have done those there are still things that can go wrong.
If so, post exactly how far you got and whether the issue is still the same or a new one.
Thank you sjpt
I de-authorised my computer and KOBO(ctl. shift D & E respectively) then re-authorised them using the same I.D. and password
then downloaded the Ebook without problem.