Ge 3:20 And Adam called his wife's name Eve, because she was the mother of all living.
21 Also for Adam and his wife the LORD God made tunics of skin, and clothed them.
22 Then the LORD God said, "Behold, the man has become like one of Us, to know good and evil. And now, lest he put out his hand and take also of the tree of life, and eat, and live forever" -
23 therefore the LORD God sent him out of the garden of Eden to till the ground from which he was taken.
24 So He drove out the man; and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life.
Adam believed in the promise of God that his wife would bear the Seed, who will be man's deliverer. His faith made him call his wife Eve, which means life or life-giver. The Deliverer would be her great, great, great grandson, her Seed.
God responded by clothing them with tunics of skin. Their fig leaves would not do. An animal had to be sacrificed to make this possible. This is a picture of salvation.
Man knew good and evil in a bad sense. He knows what is good but does not have the power to do it. He knows evil experientially and has the propensity and inclination to it.
God in judgment and mercy had to banish them out of the garden of Eden. The garden of Eden was the "Holy of holies" in their time. God's special presence was there. Because of sin, they had to be driven away from it. No sinner can dwell there.
This is to teach Moses' Israelite readers the need for a sacrifice, that sin separates from God, that God is a holy God and their need for a Deliverer.