Daniel 2:1 - Dummelow's Commentary on the Bible

The second year] seems inconsistent with the statement in Daniel 1:5, that Daniel and his companions were under training during three years of Nebuchadnezzar's reign. But it appears from the monuments that the Babylonian kings counted the year after their accession as their first year. The 'second' year might therefore be really the third, while the 'three' years of Daniel 1:5 might include, by another mode of reckoning, the year of accession, the following year, and part of the next. The 'three' years might, therefore, be over before the end of the 'second' year.