I am having trouble Deleting Libraries , I have removed some, but there are still the title there under the Libraries, see Pic, if i right click and go delete move to trash nothing happens, I have also gone into Libraries, show package contents, and remover what i can see, so where else do i go to get rid of the old Library name ?

Well, in the screen caps, you don't have a Library targeted, you have spcieifc EVENTs targeted.

Dumping Events inside Libraries won't affect the library at all. It's a container.

Trashing a Library will trash ALL the contained Events, projects, titles, clips and whetever else the Library contains, you can get rid of them by simply shutting down FCP-X - finding the Library via the finder, and dropping the whole Library into the trash - followed by the traditional "empty trash" choice.

This is massively destructive. So it's smart to backup Librareis by copying them to external drives (where the finder can't see them if they're dismounted) so that you can bring them back as needed.

Good luck.