This Ezra went up. See comment on Ezra 2:1, where the same expression ― "went up"—is used. He was a ready scribe in the law of Moses. On the meaning of this phrase, and the new position occupied by "scribes" after the captivity, see 'Introduction to Ezra,' § 5.
Which the Lord God of Israel had given. It is characteristic of Ezra's piety never to forget that the law was not a mere human code given by an earthly lawgiver, not even a national treasure, the accumulation of centuries, but a direct Divine gift "the law of the Lord" (verse 10), "the words of the commandments of the Lord, and of his statutes to Israel" (verse 11), "the law which the Lord had commanded by Moses" (Nehemiah 8:14).
According to the hand of the Lord his God upon him. i.e. "by reason of God's favour to him." God, by reason of his favour to Ezra, inclined the heart of Artaxerxes towards him, so that he granted all his request.
The nature of the "request" is not directly stated, but may be gathered from the "letter of Artaxerxes," especially verses 13, 14, 16.