They can get the permit on March 1
california
First, note that there are two different rules that exist for when someone turns a certain age:
- The "common law rule", which holds that an age is reached at the start of the day before one's corresponding birthday (so someone born August 31, 2000 would turn 15 on August 30, 2015). This rule originates in 17th-century English judicial rulings.
- The "birthday rule", which holds that an age is reached at the start of the day on the anniversary of one's birth (i.e. on one's birthday). I believe that this is how the vast majority of people in America today think about ages.
Which of these rules is in effect is often left unspecified by statute and is left to the courts to decide, like in the 2014 Michigan Supreme Court case People v Woolfolk. And the same jurisdiction may use different rules in different contexts: for example, at the US federal level, for the calculation of social security eligibility, the SSA uses the common law rule, but for criminal sentencing purposes the birthday rule is used—someone is considered a juvenile until their 18th birthday. Sometimes laws will use phrasing like "a person who has reached their 13th birthday" or "who has not yet attained their 21st birthday" instead of "a person of age 13 or older" or "under the age of 21", thereby skirting the issue.
The California Supreme Court has ruled that the California legislature intended to adopt the birthday rule for the calculation of ages.
While the California Vehicle code does not explicitly define "month", other parts of the California code (1, 2) consistently define it as "a period commencing on any day of a calendar month and extending through the day preceding the corresponding day of the succeeding calendar month, if there is any corresponding day, and if not, through the last day of the succeeding calendar month."
A person is 15 and 6 months of age when 6 months have elapsed since their 15th birthday; the six month period would extend through the final day of February (the 28th or 29th), so they would turn 15 and 6 months on March 1.
then what about a person that is born on September 01
They can get the permit on the same day, March 1.
Further Reading