Can apple down grade an iPhone 4?

Can apple down grade an iPhone 4?

Firmware speaking? Yes.

I'm not sure what you mean by 'down grade' but am assuming you meant downgrade the iOS version. That's possible, you just have to follow this guide:
http://www.redmondpie.com/downgrade-ios-6-to-5.1.1-on-a4-ios-devices-using-redsn0w/

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