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In the seventh month on the twenty-first day of the month
This is the seventh month of the Hebrew calendar. The twenty-first day is near the middle of October on Western calendars. (See: rc://en/ta/man/translate/translate-hebrewmonths and rc://en/ta/man/translate/translate-ordinal)
the word of Yahweh came
This idiom is used to introduce a special message from God. See how you translated this in Haggai 1:1. Alternate translation: "Yahweh gave a message" or "Yawheh spoke this message" (See: rc://en/ta/man/translate/figs-idiom)
by the hand of Haggai
Here the word "hand" refers to Haggai himself. Yahweh used Haggai as the agent to deliver his command. See how you translated this in Haggai 1:1. Alternate translation: "through Haggai" (See: rc://en/ta/man/translate/figs-synecdoche)
Haggai
See how you translated this man's name in Haggai 1:1. (See: rc://en/ta/man/translate/translate-names)