“in the east.” The Bible is written from the geographical perspective of Israel, so “in the east” most likely means at a place east of Israel. Although “Israel” did not exist as a nation when God put man in Eden, it did exist when Moses wrote Genesis.
“in Eden.” The Hebrew word “Eden” means “pleasure” or “delight,” and in this verse, “Eden” apparently does not refer to a garden, but rather a place East of Israel: a delightful area. In that sense, the “Garden of Eden” could be a Garden of Delight in a delightful place. See commentary on Genesis 2:15.