Wenn der FK in Posts.*_Airport_code bezieht sich nicht auf Airports.id wie MJB annimmt, aber zu Airports.Airport_code dann
SELECT
APS.Airport_name AS Source,
APD.Airport_name AS Destination,
Posts.date_of_departure
FROM Posts
INNER JOIN Airports APS ON(APS.Airport_code = Posts.Source_Airport_code)
INNER JOIN Airports APD ON(APD.Airport_code = Posts.Destination_airport_code)
