how to download music from youtube to itunesCan music downloaded from youtube on itunes be synced onto an ipod shuffle?

I just got an ipod shuffle for christmas, because I play basketball and during pre game warm-ups I like to listen to music. I have an iphone so when im running with my phone in my pocket it always manages to fall out so I thought a shuffle would be how to download music from youtube to itunesgreat to have. Anyway i'm having trouble syncing my music onto the shuffle. In my itunes library i have songs from both frostwire and youtube that I have downloaded and it seems like only the frostwire songs sync onto the shuffle. Music from both frhow to download music from youtube to itunesostwire and youtube both sync onto my iphone, so I don't get why there not syncing onto my shuffle. Does anyone know why this is? And does anybody know how to get the music I have on itunes that I got from youtube onto my shuffle? Thank you!