i've purchased songs in itunes and they won't show on my iphone and can't move them.

What do you mean 'won't show' and 'can't move them' ? If you want to redownload them on the phone then they might (depending upon your country, if they are still in the store, if you haven't moved countries since buying them, and they aren't hidden) show in the Purchased tab in its iTunes store app for redownloading on it.

If you are trying to sync them from your computer's iTunes library, then is that the computer that you sync the phone ?

Have you tried using iTunes or iTunes in the Cloud?

Sync your iPhone, iPad, and iPod with iTunes using USB - Apple Support

Sync your iPhone, iPad and iPod touch with iTunes using Wi-Fi - Apple Support

Re-download or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - Apple Support

Are there any error messages? Do you have enough space on your phone?

Take a look at this thread: Why won't my songs transfer from itunes to my iphone?

And at this article: http://www.imore.com/cant-sync-music-itunes-ios-8-try-fix

Where are you trying to drag them over from ?

If they aren't showing in the Purchased tab in the iTunes store app on your phone for redownloading, then does Music show as a category there (music can't be redownloaded in all countries) ? And you are logged in with the same account that bought them (and haven't moved countries) - that id shows at the bottom of the Featured tab in the app, and you've tried logging out (by tapping on it) and back in and seeing if they then show for redownloading ?

If they are greyed out in your computer's iTunes library then presumably they don't play there (?). If not then do they show in the Purchased link under Quick Links on the right-hand side of the iTunes store homepage on your computer's iTunes for downloading on it ? Or have you tried copying them back from your backup of your downloads/library and into iTunes (File > Add To Library).

For your phone, have you tried logging out and back into your account on it and seeing if they then show for redownloading on it ? And you are in a country where music can be redownloaded, Music shows as a category in the Purchased tab on it ?

How? I have the same problem. My iTunes Music on my Mac will not show up, sync, or allow my to transfer it over to my iPhone.

The music plays ok on that computer, and that is the computer that you sync the phone to and you aren't using iCloud Music ?