Zack's plane was a red plane owned by Norbert "Zack" Van Houten.
After Bart had called Norbert Van Houten who lives in Solvang to come to Springfield and take care about Milhouse, he went to the Springfield International Airport and thought Norbert was arriving via Solvang Air, but he didn't. He arrived in a plane, fascinating Bart.
Norbert and Milhouse used to fly around Springfield many times. Once after a trip when they parked in front of the Simpson house, the plane blew up. Norbert and Milhouse didn't care about it at all and just laughed.