"Kislev" is the ninth month of the Hebrew calendar. It is during the last part of November and the first part of December on Western calendars. (See: [[rc://en/ta/man/translate/translate-hebrewmonths]] and [[rc://en/ta/man/translate/translate-names]])
Nehemiah is referring to the number of years that Artaxerxes had been reigning as king. AT: "in the twentieth year of the reign of Artaxerxes, King of Persia" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/translate-ordinal]])