Trying to peel the paper off of garlic can be a pain. This is a great method if you don’t need your cloves to be totally whole and beautiful once peeled.
Start with garlic cloves with intact paper
One at a time, whack them with the flat of a chef’s knife or cleaver or something you’re not likely to slice your hand open on.
Smashing the garlic deforms the cloves and loosens up the skin.
Then simply remove the bits of skin, and you have peeled garlic!
Then all you hafta do is mince it (if you want), or if you’re making garlic mashed potatoes, toss the cloves in the boiling water with the potatoes, or slice it, or whatever!