The forest of Ephraim was a rocky, wooded area of land east of the Jordan River near a place called Mahanaim. The army of King David defeated Absalom in the forest of Ephraim (2 Samuel 18:6).
It is difficult to connect this location with the territory of Ephraim. The tribe of Ephraim might have once controlled land farther east, but later lost this area after they were defeated by Jephthah and the people of Gilead in a battle near Zaphon (Judges 12:1–6). This is the most probably explanation.
People might have used the name "forest of Ephraim" when Ephraimites controlled the land. Or, people might have named it later to remember Ephraim's defeat in that area. Some scholars think that (Joshua 17:14–18).