Albert Barnes Commentary Nehemiah 2:1

"And it came to pass in the month Nisan, in the twentieth year of Artaxerxes the king, when wine was before him, that I took up the wine, and gave it unto the king. Now I had not been [beforetime] sad in his presence." — Nehemiah 2:1 (ASV)

Nisan was the name given by the Persian Jews to the month previously called “Abib,” the first month of the Jewish year, or that which followed the vernal equinox. It fell four months after Chisleu (Nehemiah 1:1).

The twentieth year - As Artaxerxes ascended the throne in 465 B.C., his 20th year would correspond to 445-444 B.C.