My Ipod Nano 6th generation's screen wont show, but i can still hear music. What can I do?

Did you try this?

• Reset iPod by holding down the Sleep/Wake button and Volume Down button until you see the Apple logo appear. If the Apple logo appears on the display, connect iPod to a computer and verify that it appears in iTunes.
• If the Apple logo does not appear, or if the iPod is not seen in iTunes, try putting the iPod into disk modeand restoring:
  • Reset the device (press the Sleep and Volume Down buttons simultaneously until the display turns black—about eight seconds).
  • When the display turns black, hold down the Volume Down and Volume Up buttons simultaneously until the device enters Disk mode.
• While the device is in disk mode, connect it to iTunes and try to restore.

copied from iPod nano (6th generation): Hardware troubleshooting

If restoring did not work, you might have a hardware defect, I'm afraid.

Can you get it looked at by visiting an Apple Store? If not, get it serviced:

Apple - Support - Service Answer Center

You're welcome. Good Luck 🙂