Lunar solar terms

The eight-character lunar calendar is calculated according to solar terms. It depends on which day you were in the early winter of that year. You said you were on the second day of the tenth lunar month. If you were born in beginning of winter in 10/0, you were born before beginning of winter, so it is the moon (September). If you were born in beginning of winter in 1 year1month, then you were born after beginning of winter, that is, the moon (1year in June).