Software update on iPod touch 4th generation
The last iOS release available for iPod touch 4th generation is iOS 6.1.6. If you have a Mac or PC handy, you can install iTunes and restore the iOS firmware using it.

To download iOS 6.1.6 firmware for your iPod touch 4th generation, visit IPSW.me, select your device and click download. Make sure the firmware you select is signed. (Alternatively, you can use this link to download directly).

The firmware is downloaded from Apple's server and safe to use. They are digitally signed and are verified by Apple while installing.