"June 9th" is thought to be a reference to the date in which the report on the Challenger disaster was released. This date is also the ninth day of the sixth month, a reference to the "69" theme throughout some of BoC's other music.
In numerous interviews, Boards of Canada have referred to "Red Moon nights", free-form outdoor gatherings with friends, music, movies and bonfires that Hexagon Sun has celebrated for years. The Red Moon incident appeared to reference an event on June 10th, 2006. Also, the album Tomorrow's Harvest was released on June 10th, 2013. It's possible that the Red Moon party is held around this time each year. Assuming the event is held on a Saturday, the latest time June 9th falls on a Saturday before this song was released would be in 1990.