How to transfer Apple music playlist to an iphone ?

I have tons of playlist of music i purchased and one of the perks to Apple Music was to be able to add albums to a playlist I have already made. When i add it on the computer and try to sync that playlist it says cant sync this song because apple music doesn't transfer it Iphones ?? Smh isn't that the purpose of this service. Does anyone have any info cause apple doesn't seems to know whats going on.

All i want is my music that i have plus apple music together in one playlist so i can plug into my car and listen without streaming