Is it possible to shut down an Ipod nano 6th generation?
According to Apple Support:


  If the iPod nano is paused, and you
  press the Sleep/Wake button to turn
  off the screen, the following behavior
  will take place:
  
  
  For 36 hours after pressing the Sleep/Wake button and turning off the
  screen, iPod nano is in Standby, and
  will quickly wake up when you press
  the Sleep/Wake button again.
  After 36 hours in Standby with no activity, iPod nano will shut down
  automatically. Pressing the Sleep/Wake
  button after iPod nano is shut down
  will turn on iPod nano, and boot to
  the main Home screen.
  (Your iPod nano is considered paused if there is no music or FM radio playback, or an active pedometer session.)
  


Additional Information


A fully charged iPod nano provides up to 24 hours of music playback time.