Q: new playlist won't sync

Greetings Donna and Mark,

Welcome to the Apple Support Communities!

I understand that you are trying to sync a playlist from iTunes to your iPhone. The following two articles explain how to sync content in two different ways. If you are unable to manually move the playlist to your iPhone or sync through the device menus, please give me more information on your situation. 

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

Manage content manually on your iPhone, iPad, and iPod - Apple Support

Cheers,

Joe