# Ezra had established his heart to study
"Ezra committed his life to study". The people no longer know the law of Moses. Therefore, the king allows Ezra to return to Judea to teach the people about God's law. Many people go with him.
# carry out
"obey"
# the law of Yahweh and to carry out and teach its statutes and decrees
These were the laws that God passed down to Israel through Moses.