Can you explain this regarding the time of the birth of Jesus?

As we all know as the story goes Jesus was borne during the reign of King Herod the Great when he ordered the killing of the children, then in Luke 2:1, it says that the birth of Jesus was when the census was taken throughout the Empire and Quirinius was the governor of Syria, that was sometime in 6AD, but historically Herod already died in 4BC and that's 10 years apart.