It depends on how you view the millenium. If you take the counting system of the Gregorian calendar (the calendar in popular use worldwide), the millenium begins with the year ending in '1', based on the idea that Christ was born in the year 0, so the first year after His birth would be the year ending in *!, and the years ending in *1, *2, *3, *4, *5, *6 are the first six years of a millenium. By the Gregorian calendar, Leila would have to be born on 6/6/2006 for her birthdate to equal 6/6/6. However, the International Organization for Standardization (ISO) uses the astronomical calendar, which sets the first year of the millenium at '0', so the years ending in *0, *1, *2, *3, *4, *5 are the first six years of a millenium. This movie has, apparently, used the ISO standard, making the date 6/6/2005 equal to 6/6/6. More information about the dating of a millenium can be found here and here.