7:6a this Ezra came up from Babylon.

This man Ezra departed from Babylon.
-or-
Ezra went up ⌊to Jerusalem⌋ from Babylon.
-or-
I left Babylon and journeyed/traveled ⌊to Jerusalem⌋.

7:6b He was a scribe skilled in the Law of Moses, which the LORD, the God of Israel, had given.

He was a scribe who knew very well the Law which Yahweh, the God of Israel, had given/revealed to Moses to write.
-or-
He was a copyist/writer of and an expert in the Law that was written down by Moses. Yahweh, the God of Israel, had given the Law to his people.
-or-
I was skilled in reading and writing and a scholar/expert in the books that Moses wrote. Those books contain the laws that our (incl.) God, Yahweh, gave to us Jews.

7:6c The king had granted Ezra all his requests, for the hand of the LORD his God was upon him.

The King had given Ezra everything which he had asked for because the hand of his God, Yahweh, was upon him ⌊to give him success⌋.
-or-
⌊Before Ezra left,⌋ Chief ⌊Artaxerxes⌋ gave him everything he requested from him, because Yahweh, the God Ezra worshiped/served, was blessing Ezra.
-or-
Yahweh my God was helping me. So he caused ⌊Artaxerxes⌋ the ruler ⌊of Persia⌋ to give me everything I asked him to give.

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