23:32a So the Levites were to carry out the responsibilities for the Tent of Meeting

So the Levites did everything that they were supposed to do. They took care of the Holy Tent (English Easy-to-Read Version)
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So the Levites had special work. They had to keep the place where people met God (Easy English Bible)

23:32b and the Holy Place, and, under their brothers the descendants of Aaron,

and the Holy Place. And they helped their relatives, the priests, Aaron’s descendants, (English Easy-to-Read Version)
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and its holy place clean. And they had to help their cousins, Aaron’s descendants (Easy English Bible)

23:32c the service of the house of the LORD.

with the services at Yahweh’s Temple.
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with their work in Yahweh’s house.

23:32a–c (combined)

So the descendants of Levi did the work that was assigned to them by their fellow Israelis who were descendants of Aaron. They did that work in the area surrounding the Sacred Tent, and in the Sacred Tent, and later at the temple. (Translation for Translators)
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In short, the Levites had thee main areas of work. ⌊First,⌋ they watched over the Holy Tent. ⌊Second,⌋ they cared for the Temple. ⌊Third,⌋ they helped the priests, Aaron’s descendants, in their service of Yahweh.

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