Do you subscribe to iTune Match? If you do, did you turn ON iTunes Match on the iPod touch? That can remove your songs that are currently synced directly from the computer's iTunes library, and prevent direct syncing with the computer's iTunes library (because the iPod touch is now syncing to your iCloud Music Library). iTunes Match is compatible with iOS 6.1.6.
If iTunes Match is not involved, select the iPod touch in iTunes (click its device button on horizontal bar) to show its settings screen in iTunes window. Along the left side (in the sidebar), under Settings, click Music. To the right, the iPod's Music settings screen is shown.
Is the checkbox for Sync Music checked? If you want iTunes to automatically sync songs to iPod, Sync Music needs to be checked. On that screen, you can set up how iTunes syncs songs to the iPod. If your complete iTunes music library can fit on the iPod, you can choose to sync Entire music library. Otherwise, choose to sync Selected playlists, artists, albums, and genres. Then, choose the portion of your iTunes library that you want iTunes to sync from the lists below. For example, you can create playlists (in your iTunes library) for your iPod, and select them on the iPod's Music settings screen. When you click Apply, your selection syncs to the iPod. Going forward, iTunes keeps the iPod "in sync" with your iTunes library, based on how you set up the iPod's Music settings screen.
For videos, select Movies or TV Shows (whichever category your videos belong to), in the sidebar of the iPod's settings screen. Like with Music, set up those screens as desired.
If you previously loaded songs manually, by dragging and dropping songs (and other items) on iPod in iTunes, and did not use automatic syncing (as described above), please post back.
