4:7a Solomon had twelve governors over all Israel

Solomon chose/appointed 12 governors/overseers over all ⌊the land/people of⌋ Israel.
-or-
Solomon ⌊also⌋ placed twelve (12) men/officers in charge of the twelve (12) regions in Israel.

4:7b to provide food for the king and his household.

These governors/overseers had to provide food for the king and the members of his household.
-or-

⌊Their job/duty was⌋ to support the king and all his dependents by giving them food.

4:7c Each one would arrange provisions for one month of the year,

Each governor/overseer was responsible for providing this food for one month each year.
-or-
Each officer had/received this job/duty for one month per year.

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