Q: How do I sync the music that is on my iPod Nano onto my Mac?

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Officially, Apple only lets you transfer the songs you got from the iTunes Store. See -> Redownload or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - Apple Support

If you need to transfer songs that you did not purchase from the iTunes Store, have a look at Zevoneer's reply -> Copy music from Ipod to new computer...