Now after the death of Jehoiada …: The common Hebrew conjunction rendered Now may be translated “But” (Good News Translation, New Living Translation, NASB) to mark contrast, since the conduct of Joash in the following verses is very different from his behavior during the lifetime of Jehoiada.
The princes of Judah came: For princes see verse 10. They came most likely to the royal palace.
And did obeisance to the king means they bowed down before the king as a sign of their loyalty to him (see the comments on 1 Chr 21.21). Nova Tradução na Linguagem de Hoje adds the implied information that bowing before the king was done “as a sign of respect.” Good News Translation omits this whole clause, which is not recommended.
Then the king hearkened to them: The verb hearkened is somewhat archaic English for “listened to” (New Revised Standard Version). This clause may be rendered “Then the king followed their advice.” The text does not say explicitly what the leaders of Judah said to the king, but the following verse strongly suggests that they indicated that they wanted to worship other gods. Moffatt makes this connection more explicit by translating verses 17 and 18a as follows: “Then, after the death of Jehoiada, the nobles of Judah went with a petition to the king, 18 by whose permission they abandoned the temple of the Eternal the God of their fathers, and worshiped sacred poles and idols.”
Quoted with permission from Omanson, Roger L. and Ellington, John E. A Handbook on 1-2 Chronicles, Volume 1. (UBS Helps for Translators). Miami: UBS, 2014. For this and other handbooks for translators see here .
