'Years' in the Bible

Now in the first year of Cyrus king of Persia [that is, the first year he ruled Babylon], in order to fulfill the word of the Lord by the mouth of Jeremiah [the prophet], the Lord stirred up (put in motion) the spirit of Cyrus king of Persia, so that he sent a proclamation throughout all his kingdom, and also put it in writing, saying:

In the second year of their coming to God’s house at Jerusalem, in the second month, Zerubbabel the son of Shealtiel and Jeshua the son of Jozadak began [the work], with the rest of their brothers—the priests and Levites and all who came to Jerusalem from the captivity. They appointed the Levites, from twenty years old and upward, to oversee the work of the house of the Lord.

They replied, ‘We are servants of the God of heaven and earth, and are rebuilding the temple which was erected many years ago, which a great king of Israel built and finished.