How can I remove a broken plastic packing nut from a faucet?
I'm assuming this is in reference to an outdoor garden faucet. If you can't get the old packing out, replace the entire faucet. But first, make sure you don't have a dope of a builder that would solder the threads. Try to unscrew the fixture from the wall (shutoff the outside water first). If it unscrews, then all you need to do is pickup some pipe dope and a new faucet from the store. Clean the old threads, put some pipe dope on the threads, and screw on the new fixture.