Delete songs from i pod touch 2nd generation - Apple iPod Touch 8GB 32GB 64GB 3rd Generation iTouch Zebra Skin Case Cover Protector Pink and Black

You can follow the below steps to delete songs from iPod Touch.

Unlike ancient iPod models, iPod touches are given the new function of deleting songs directly from the device like any iPhones and iPads, which means that you are able to delete songs one by one from the Music app or delete all songs from the Settings app on the iPod touch. The following steps will introduce you how to delete music from iPod touch directly.
For the iPod touch running iOS 8.3 and before:
Open Music app > Select Songs along the bottom > Find the song you want to remove > Slide to right until the Delete button shows > Tap on Delete to delete the selected song.
For the iPod touch running iOS 8.4 and later:
Open the Apple Music app > Select My Music along the bottom > Tap the song you want to delete > Click "..." next to the song name > Click Delete and confirm that you want to delete the song from your iPod touch.
Or you can delete all songs from iPod touch in Settings: Launch Settings > General > Usage > Manage Storage > Music > Edit > Click the red minus icon > Delete.

For more methods, check: Top Three Ways to Delete Music from iPod/iPod touch

You must connect to the computer with iTunes. There you can select the music you want t delete.
For that wait till the iPod is backed up by iTunes, then on the left side click on the line with the name of your iPod. Then on top click on Music and then you see what music you can synchronise.
If you already did remove the original backups from the music on the iPad, there is a chance iTunes all remove all these numbers.

Apple has lots of info about every part you want to know about your iPod and iTunes.