on which network was it aired?
Fox network
Meet the Quagmires
 It originally aired on Fox on May 20, 2007.
what is 'meet the quagmires'? It is the 18th and final episode of the fifth season of the animated comedy series "Family Guy". who wrote this episode? Mark Hentemann
wiki:11008363
Meet the Quagmires [SEP] Introduction
"Meet the Quagmires" is the 18th and final episode of the fifth season of the animated comedy series "Family Guy". It originally aired on Fox on May 20, 2007. The episode features Peter after he goes back in time, in order to live the single life a little longer, before he meets future wife Lois. This causes Quagmire to make his own move on Lois, and they ultimately end up marrying and having children; Peter is horrified by this "alternate timeline" and resolves to go back in time again and set things right. The episode was written by Mark Hentemann and directed by Dan Povenmire and Chris Robertson.