“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” (#05731 עֵדֶן) 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.