“went out in surrender to the king of Babylon.” Jehoiachin left the walled city of Jerusalem and surrendered to Nebuchadnezzar. This was 597 BC, and Ezekiel was in this captivity and taken to Babylon at this time (Ezek. 1:2).
“in the eighth year of his reign.” That is, in the eighth year of Nebuchadnezzar’s reign. Jehoiachin only reigned for three months (2 Kings 24:8).