Albert Barnes Commentary 1 Samuel 15:12

"And Samuel rose early to meet Saul in the morning; and it was told Samuel, saying, Saul came to Carmel, and, behold, he set him up a monument, and turned, and passed on, and went down to Gilgal." — 1 Samuel 15:12 (ASV)

A place - Rather, “a monument.” The Hebrew word יד yâd means a “hand,” but is used in the sense of “monument” or “trophy” in 2 Samuel 18:18, where we are told that the marble pillar which Absalom set up in his lifetime was called “Yad Absalom.”

Carmel - This location would be on Saul’s line of march on his return from the country of the Amalekites, especially if he came from the neighborhood of Akaba.