Can I Downgrade iPod touch 4?

Downgrade is Currently Not Supported
Apple is currently only signing iOS 6.1.6 for iPod touch 4. The signing window for iOS 6.1.5 and all earlier releases has closed.
Apple permanently closes the signing window for older releases within 1 to 2 weeks of launching a newer update. Because Apple's servers authenticate each restore online, trying to install any previous iOS build on iPod touch 4 will immediately fail with iTunes Error 3194.
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Can I downgrade from an iOS Beta on iPod touch 4?
Yes. If your iPod touch 4 is running an iOS Beta, you can always restore back to the latest signed public release using Recovery Mode in Finder (Mac) or iTunes / Apple Devices (Windows).
Can I downgrade to the iOS version iPod touch 4 originally shipped with?
No. Apple permanently closes the signing window for older releases. Even though iPod touch 4 originally launched with an earlier version, Apple servers will no longer authenticate that installation.
What can I do if I cannot downgrade iPod touch 4 but experience battery or performance bugs?
You can perform a clean restore to the latest signed firmware using a computer to eliminate software glitches and corrupted cache, or await the next minor point update from Apple that includes targeted bug fixes.
Can I downgrade iPod touch 4 if the signing window has closed?
No. Apple servers reject restore verifications for unsigned builds (returning iTunes Error 3194). Unsigned firmware cannot be installed on standard Apple devices.
Will restoring or downgrading iPod touch 4 erase data?
Yes. Flashing an IPSW firmware file requires a restore that wipes on-device storage. Ensure your personal data is backed up to iCloud before proceeding.