## On the eighth day ##

This could be translated as "On the eighth day after the baby was born" or "When the baby was eight days old."

## they ##

This could be translated as "Zechariah's and Elizabeth's friends and relatives" or simply as "people."

## to circumcise the baby ##

This could be translated as "for the baby to be circumcised" or "for the baby's circumcision ceremony." One person circumcised the baby, and the others were there to celebrate with the family.

## they would have called him ##

"they were going to name him" or "they wanted to give him the name"

## after the name of his father ##

This could also be translated as "like his father" or "his father's name."

## by this name ##

Since Elizabeth had said the name and they were talking to her, this could be translated as "by that name."