Adding playlists to iPod Nano 6th generation
You can! When your iPod is connected to iTunes, it should appear in the sidebar. Select it, and make sure  is checked.

Now, create a playlist with the + button at the bottom right of the window, and name it what you will. Simply drag the songs you want the playlist to contain over to the sidebar, and drop them in!

When you've finished, be sure to press the ⏏ button to the right of the iPod's name before you disconnect the cable.