We are using iPhoto 11 and are unable to download pictures from out mac to our iPhone 6

You use iTunes to sync photos from a Mac to an iPhone. See the iTunes section of Keep your photos safely stored and up to date on all your devices - Apple Support

We are having trouble syncing my wife's iMac Pro with her iPhone 6. Her computer has iPhotos 11.

What are the settings on your wife's iPhone 6?

Does your Wife's iPhone have iCloud Photo Library enabled? Then she cannot use iTunes Photo sync. It will be disabled. In that she should either stop using iCloud Photo Library on the iPhone or use the iCloud Web Interface at www.icloud.com and the Photos.app there to upload her photos to iCloud Photo Library and then to the iPhone. But with iPhoto '11 it would be much mor convenient to not use iCloud Photo Library.