A half-birthday is a day approximately six months before or after the anniversary of a person's birth.
The easier but less precise method is to take the number of the date of the birthday and advance the month by six: e.g. April 20 becomes October 20.
A good example where this doesn't work is six months after an August 30 birthday would be February 30, which is nonexistent in the Gregorian calendar.
Accurate calculations require the addition or subtraction of half the number of days in a year from the birth date taking into account if the time period includes a leap day or not.
This method would lead to a March 1 or February 29 half-birthday for an August 31 birthday, depending on whether it's a leap year.