As the moon orbits the Earth, its gravity pulls on the Earth, just like any other mass object in the universe pulling on another object. Because oceans cover such a large portion of the Earth, this pull by the Moon has an observable effect, which we call tides. This pull causes slight bulges of the oceanic mass. Because the Earth rotates faster than the Moon orbits, these bulges of the ocean are always ahead of the Moon. In effect, the Earth's tides pull back on the Moon, pulling it forward. This pull forward causes the Moon to gain energy and gradually spiral outward. As a result, the Moon moves away from the Earth a little bit each year, about an inch and a half a year, presently.
The Moon is about 400,000 km away from the Earth right now. Studies of tidal rhythmites have shown that the rate of recession of the Moon was about the same throughout geologic time.
6000 years ago, the Moon would have been closer to the Earth by about 250m (800ft). This small change would not cause any significant changes to the Earth-Moon interaction, and Adam and Eve were not effected..