Taken from the IMDB trivia entry for Donnie Darko:
The movie takes place in 1988. Frank tells Donnie the world will end
in 28 days, 06 hours, 42 minutes, and 12 seconds. If you add these
numbers, the sum is 88. When Samantha asks when she can have kids,
Donnie says: "Not until 8th grade." Donnie mentions to his therapist
that his dog Callie died when he was eight. (He is later seen holding
a stuffed toy dog in her office.) Donnie jokes about the Back to the
Future DeLorean which had a speed of 88 MPH. According to the
television reporter, the fire at Jim Cunningham's house was
extinguished "sometime after 8:00 last night." The red-eye flight that
almost crashes is Flight 2806 which boards at Gate 42 at 12 AM. The
climax of Donnie Darko occurs one week before the 1988 US presidential
election, when George Bush won on November 8, 1988 11/08/88. The movie
was shot (for a budget of less than US$5 million) in 28 days. There
are 28 scenes in the director's cut of this film.
Frank says the world will end in "28 days 6 hours 42 minutes 12
seconds." That figure is not random: it comes from adding or
subtracting 1 from each part of the figure 27d 7h 43m 11s, which is
the precise length of one lunar month (by one of the less-used
definitions - sidereal instead of the usual synodic).
Take away from it what you will.