Summary
Since Apple no longer signs iOS 6, you cannot use iTunes. The most reliable community tool is Legacy-iOS-Kit Requirements: downgrade ipod touch 5 to ios 6
However, there is a critical caveat: This tool was primarily functional during the windows when iOS 6.1.3 was still signed or when the OTA ticket mechanism was exploitable. Review: Downgrading iPod Touch 5th Generation to iOS
If everything goes right, you will be greeted by the iconic "Set Up Your iPod" screen on iOS 6.1.3. downgrade ipod touch 5 to ios 6
It installs iOS 6 alongside iOS 9. When you turn the device on, you click an app to "boot" into iOS 6.