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Hayley convinces Francine to get reacquainted with an old friend and after joining them in a night of heavy drinking, winds up in the hospital in need of a kidney transplant.
Upon hearing the news Stan is willing to donate one of his kidneys but Francine confesses that Hayley may not be his daughter due to a bachelorette party indiscretion.
In order to find the man who is the right kidney match, Stan and Francine travel back in time to discover who she slept with on that fateful night.
Stan and Francine go back in time to 1996 just days before they get married and Francine gets pregnant with Hayley, however, in the 2009 Season 5 episode Shallow Vows, Stan & Francine are about to celebrate their 20th wedding anniversary and Hayley's stated age is 18 both of which couldn't be true if this episode takes place in 2012.
Unless we're supposed to presume Shallow Vows took place in 2016 and although not officially stated, Hayley is now 20.
In the Season 4 episode Delorean Story-An, Stan states he has no idea what Back to the Future is but the 1996 Stan uses the movie to simplify the time travel explanation.
After we see Hayley's kidney fail, the Ultimate Kelly glasses and the glass Hayley put down have vanished.