Albert Barnes Commentary 2 Kings 3:8

"And he said, Which way shall we go up? And he answered, The way of the wilderness of Edom." — 2 Kings 3:8 (ASV)

The most direct and natural route was across the Jordan River near Jericho into the Arboth-Moab (the plains of Moab), and then along the eastern shore of the Dead Sea to Moab proper—the region south of the Arnon River.

However, the route they chose was the one that led to the land of Edom: around the southern end of the Dead Sea and across the Arabah, the valley that extends south from the Jordan River and the Dead Sea. This would allow them to join forces with Edom, which had resumed its dependence on Judah, even though the year before it had been in alliance with Moab (2 Chronicles 20:22). This strategy would let them come upon the Moabites unprepared.