Q: why can' t I sync my ipod with my itunes. It says computer is not authorised to play purchased items but the computer is authorised...help please

Hello there maisymaher,

It sounds like you have used your Apple ID to authorize your iTunes library to be able to sync your content to and from your computer, but you are still being prompted to authorize the computer. I would start with this article about that very sort of issue where iTunes might repeatedly request you to authorize the computer:

If iTunes repeatedly prompts you to authorize your computer

Otherwise this indicates that at some point another Apple ID downloaded something to your phone, whether it was an app, a movie, a song, a TV show, or just about any sort of content that requires that an Apple ID be signed into Settings > iTunes & App Store on your iPod Touch.

What I would suggest is, if you have any other possible email address that might be Apple IDs, or if you had changed your Apple ID email address to something else try authorizing iTunes with those email addresses and using any passwords you can think they might be.

If you remember the email address but not the password you may need to reset the password for that account using this article:

If you forgot your Apple ID password

If you know what content is causing this to happen you can also delete the content from the phone to allow it to sync. 

Delete music, movies, apps, and other content from your iPhone, iPad, or iPod touch
 

Thank you for using Apple Support Communities, let us know how that goes!