Rashi and Radak, citing Targum Yonasan: It is in a noose and in chains.

Malbim: Yeho'achaz was put only in Chachim, via which they draw a Chayah outside of its abode. They put Yehoyakim in Soger, which is extra guarding, and brought him to Melech Bavel.

Rashi: They incarcerated him there. Radak - these are strong towers. The same applies to "Metzados Sela'im Misgabo" (Yeshayah 33:167), "bi'Mtzados Ein Gedi" (Shmuel I, 23:29).

Malbim #1: Melech Bavel conquered him twice. The first time he was a slave, and he sent him free. The second time, he put him in Metzados.

Malbim #2: They put Yehoyakim in Soger, and Yehoyachin in Metzados. Both of them are considered one kingship, like I explained above (refer to 19:5:5:1*).

Radak: This is because it said above (7) "mi'Kol Sha'agaso."

Malbim: [Yehoyakim and Yehoyachin] did not return to Eretz Yisrael.

Radak: "El" is like Al. If this refers to Tzidkiyah, this is proper, for he did not return to Eretz Yisrael from when he was exiled. Also if it refers to Yehoyakim, it is proper, for also in his first Galus, Melech Bavel put him in Metzados, lest he return to Eretz Yisrael. Even though he returned him afterwards, that is because he thought that he will not rebel, and he trusted him. In his second Galus, Kasdim seized him to take him to Bavel, and he died on the way - "Sachov v'Hashlech me'Hal'ah l'Sha'arei Yerushalayim" (Yirmeyah 22:19). Some explain that he died in Bavel.

Radak: Yehoyachin was omitted, for he ruled only three months. Tzidkiyah was omitted, for he and Yehoyakim ruled the same amount (11 years), and both were given to Melech Bavel and died in his Reshus, so [the Mashal] was said about both of them together. The primary Churban began from Yehoyakim, for Melech Bavel took with him to Bavel some of Klei Beis Hashem and officers of the land.

Malbim: Perhaps Yehoyachin is included, for he ruled with Yehoyakim (refer to 19:9:2:3).