As you can tell, there is a "whole" clove buried under the smaller outer layers. My question is - do you just take out the whole, smaller clove and use it, or do you use the outer layers as well? Do the outer layers have a different flavor? Are they bitter?
I think that might be elephant garlic, which isn't really garlic at all. It's in the same family, but is actually a kind of leek so it has a flavor that's a cross between garlic and onion, but milder than garlic. Because it's not very strong you'll probably want to add the whole thing. Just chop it and use it as normal.
You can generally use the whole thing unless there's another papery skin inside in which case discard that (some garlic may go with it) or anything that seems bad (soft or discoloured). I've never noticed a difference in flavour, and I normally crush mine. I prefer big garlic when I can get it, for convenience when preparing as I tend to use a fair bit at a time.
Elephant garlic is super easy to grow, and the flavor is milder, so use the entire clove. If in doubt, slowly cook in a toaster oven ahead of time to make sweet and gooey (and leave your home smelling amazing).
To grow elephant garlic, take 40 of these cloves that are in good condition and pre-soak in water while you roto-till a patch of your lawn, large enough to make an 8 in x 8 in space for each, preferably as close to a square grid as possible, with 8 inches to spare all the way around. Do this ideally in September. I used a sod cutter to remove the grass and move to areas of the lawn that needed them. If in doubt, however, add seed-free grass clippings to the soil you are roto-tilling, esp, if it is full of clay. A sunny spot at least part of the day is best.
Plant your little bulbs according to how you should plant garlic in the fall, possibly with a little bulb-fertilizer. Planting in the Fall allows your bulbs a critical head start over grass in the Spring. Once you get pre-flowers, get out the scissors and snip yourself a stir fry with a little butter. Yum! Your 40 little "steers" will now focus on bulb making. I got a 100% yield my very first year in SE Michigan -- 40 little elephants! I dug a couple a little early as needed, and to check on progress.
Just in case you might get irradiated product from a corporate supplier, lean toward buying your parent elephant garlic from an organic/roadside source.