Rashi #1: It teaches that there were tunnels under these chambers.

Rashi #2: It teaches that there were chambers in the east of the Chatzer. It says umi'Tachas because the Mikdash was on a mountain, and in the east was lower. The verse means, in the lower part of the Chatzer, in the entrance from the east, when he comes to there from Chatzer ha'Chitzonah. Radak - it already taught that these chambers reached only until half the length of the Heichal. Here it teaches that they were in the east.

Malbim: It already taught that one who left Ezras Yisrael via the Ulam and went from south to north to Lishkos ha'Chamishim, he entered via one Amah open between the head of the Geder and the head of Lishkos ha'Chamishim. He left the opening of Lishkos ha'Chamishim to the north to Chatzer ha'Chitzonah in front of the Ritzpah and the chambers by the north wall. Now it says that one who comes to here from east to west, he enters the eastern gate of Chatzer ha'Chitzonah and goes west. The path to these chambers was under the chambers, i.e. from the east, which was lower on the mountain.

Radak: This is one of three pairs of words in which the first letter of the latter word is put at the end of the first word.

Radak: The entrance was in the east, for one enters Har ha'Bayis from the east, and from there inside, until the Ulam.

Vilna Gaon: This refers to one who comes from the east.

Radak: This is a noun (entrance). The pronunciation discusses one who comes via there.

Vilna Gaon: This refers to one who comes from the east to the chambers mentioned above.