When I'm older, this is the kind of lifestyle I want to live (food wise) with this being mainly what I eat.I'm sure my other family members would eat from other sources besides what we would have there, but if not, could a large garden and hen coop of say 6 hens keep a family of 4 full every day? (I've never had a garden before but am definitely going to in the future, insight please.)
Well sure... our ancient ancestors had to do this. Hard to know what sort of land you'd need. You'd have to grow some root crops like potatoes, beets - stuff that keeps for a LONG time. And you'd have to dig a root cellar. So there would be a lot of careful calculation in surviving a winter on your garden and chickens alone. We're not used to doing that anymore because of stores and trucked-in food.
My father raised chckens and we were a family of 4 but he had more than 6, I would say at least a dozen. If you don't live where you can grow food all year you will have a problem. Also you would have to grow some fruit trees. This is the place you may want to research for your future venture.
Yes, it is, if you have enough land. I have a book that discusses doing exactly that. If you have 1/4 acre for garden and animals, and cultivated that garden properly so it produces as much as possible, you could probably get pretty close. Easier with more land, of course. You might want a few more hens. If you want to learn more about it, google self-sufficiency from a garden. Keep in mind that in most climates, you can't grow food year-round so must preserve it in some way to eat in the off-season.
Not for very long on that type of diet. Hens lay for a while but they are cyclic during the winter. This means you have fewer eggs every day. During the laying season 1 egg per hen is the most you will get, during the winter it is more like 1 egg for 3 hens. To provide food for a small family you need land that can be cultivated 80 or so acres per person is a rough estimate and that takes a lot of work to prepare the land, plant and grow and then harvest. I suggest you read about home gardens and square foot gardening and try your own home garden next season.