Albert Barnes Commentary Numbers 21:4

"And they journeyed from mount Hor by the way to the Red Sea, to compass the land of Edom: and the soul of the people was much discouraged because of the way." — Numbers 21:4 (ASV)

The direct route to Moab through the valleys of Edom having been closed to them (Numbers 20:20–21), they were compelled to turn southward. Their course lay down the Arabah; until, a few hours north of Akaba (Ezion-Geber), the Wady Ithm opened a gap for them in the hostile mountains, allowing them to turn to their left and march northward toward Moab (Deuteronomy 2:3).

Thus, for some days (see note on Numbers 22:1), they were in the Arabah, a mountain plain of loose sand, gravel, and detritus of granite. This plain, though sprinkled with low shrubs (especially near the mouths of the wadis and the courses of winter torrents), furnishes extremely little food or water and is often troubled by sandstorms from the shore of the gulf. Hence, the soul of the people was much discouraged because of the way.