Can’t download music I purchased long time ago on my desk top with different email address and password on my iOS devices

Hi there, Lasfar!
Thanks for reaching out to the Apple Support Communities! It sounds like you are trying to download purchases made with a different Apple ID and you have forgotten the password and I am happy to help out! Since you have forgotten the password, I recommend taking a look at this article If you forgot your Apple ID password. This article has the best steps to reset your password along with a helpful link in case you have forgotten your Apple ID as well. Once you have reset the password and are able to access the Apple ID, you can follow these steps to Redownload apps, music, movies, TV shows, and books from the iTunes Store, iBooks Store, and App Store.
Cheers!