What you're talking about is a calculation based on the birth of John the Baptist. John the Baptist's father was a priest in the order of Abijah and John the Baptist was conceivced with his father's barren wife as a reward for his service in the temple. His service would have ended in June. The angel Gabriel visited Mary in the sixth month of that pregnancy to tell her that she would birth Jesus. The calculation is June + 6 = Dec + 9 = September.

December is definitely not the correct month because the story has shepherds tending their flocks in the field. Sheep have to be brought in from the field for the winter months and would not have been in the field in December. They would have been moved to shelter no later then the end of October.

The year is also problematic. Jesus was born during the reign of King Harrod who died in 4BCE. And during a mass killing of babies which, if it happened at all, would have occurred at least a couple of years before Harrod's death.

It's also worth saying that there isn't good evidence for Jesus having ever existed at all. It seems most likely that he did and was a reformist rabbi that the myth was built around but no one apparently wrote anything about him for a century or two after his death.