3:8a In the second month of the second year after they had arrived at the house of God in Jerusalem,

It became/was the second month in/of the second year after the people arrived in Jerusalem at ⌊the site of⌋ the house of God.
-or-
⌊The work of rebuilding the temple of God began⌋ in the second year after they arrived in Jerusalem. It was in ⌊the month of Ziv,⌋ which is the second month ⌊of the Jewish year/calendar⌋.

3:8b Zerubbabel son of Shealtiel, Jeshua son of Jozadak,

Zerubbabel the son of Shealtiel, Jeshua the son of Jozadak,
-or-
Zerubbabel, son of Shealtiel, and Jeshua ⌊the high/leading priest⌋, son of Jozadak, ⌊began to rebuild the temple⌋.

3:8c and the rest of their associates including the priests, the Levites, and all who had returned to Jerusalem from the captivity,

the priests, the men of ⌊the clan of⌋ Levi, and everyone who had returned to Jerusalem after being forced to live abroad
-or-
The other priests and the descendants of Levi and the rest of the people who had returned to Jerusalem from Babylon

3:8d began the work.

started to build ⌊the house of God⌋.
-or-
⌊joined them⌋ in the work.

3:8e They appointed Levites twenty years of age or older to supervise the construction of the house of the LORD.

They gave the task/responsibility to guide/organize the work of building the house of Yahweh, to men of Levi who were twenty years old or older.
-or-
Descendants of Levi who were at least twenty years old directed/led the work. They showed/instructed the other people/workers what to do as they worked on the temple of Yahweh.

© 2020 by SIL International®
Made available under the terms of a Creative Commons Attribution-ShareAlike 4.0 License (CC BY-SA) creativecommons.org/licenses/by-sa/4.0.
All Scripture quotations in this publication, unless otherwise indicated, are from The Holy Bible, Berean Standard Bible.
BSB is produced in cooperation with Bible Hub, Discovery Bible, OpenBible.com, and the Berean Bible Translation Committee.