'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:

Now in the second year of their coming unto the house of God at Jerusalem, in the second month, began Zerubbabel the son of Shealtiel, and Jeshua the son of Jozadak, and the remnant of their brethren the priests and the Levites, and all they that were come out of the captivity unto Jerusalem; and appointed the Levites, from twenty years old and upward, to set forward the work of the house of the LORD.

And thus they returned us answer, saying, We are the servants of the God of heaven and earth, and build the house that was builded these many years ago, which a great king of Israel builded and set up.