how to delete songs from nano 6th generation?

You do it through iTunes. If your iPod is set up for autosync, simple configure your iPod not to sync the particular songs you wish to delete from your iPod. Or if you have your iPod set up to only sync checked songs and videos, remove the tick marks next to each track you no longer want on the iPod and resync it.

Otherwise, if you manually manage its contents, you'll can manually remove these tracks from the iPod in iTunes. Plug the iPod in, click the small black triangel on the right of it from under the Devices section in the left pane of iTunes. This should open up a submenu. Click music and then when you find a track you wish to remove, simply highlight it and press Delete or right->click on it and choose Delete.

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