“Beeroth.” The word means “cisterns,” and it is the only one of the towns that has not been positively identified today.
“on the third day.” Again we see here the theme of three days (see commentary on Josh. 9:16). Israel could reach Gibeon in one day, because the army of Israel went from Gilgal to Gibeon in one night (cp. Josh. 10:9). However, this trip in Joshua 9:17 was much less rushed. Furthermore, Israel was going into the heart of enemy country and did not want to be ambushed, so they took time to prepare to leave and took time in the journey, and likely kept sending scouts ahead of the people to report on the situation.
“Gibeon, Chephirah, Beeroth, and Kiriath-jearim.” All of these cities except Beeroth have been positively identified (and Beeroth is likely known). They are not quite 10 miles northwest of Jerusalem in the tribal area of Benjamin, and lie in a line that runs basically from Gibeon southwest to Kiriath-jearim.