"The One Where Ross Hugs Rachel" is the second episode of the sixth season of Friends, which aired on September 30, 1999.
Ross tells Rachel that he got the annulment, but he confesses to Phoebe that he didn't because he doesn't want to have three failed marriages. Phoebe proves to Ross that it isn't that big of problem: they tell the whole story to a group of girls, none of whom seem to care too much about the three divorces, however one of them insists she wouldn't date him while he's still married and another says that she thinks he's still in love with Rachel, which Phoebe insists is true. Ross insists that isn't true and decides to get the annulment, but it turns out that won't be as easy as he'd hoped because they both have to appear before a judge in order to have the marriage annulled.
Chandler and Monica tell everyone they're going to move in together. Joey is really upset about Chandler moving out because Chandler is the best roommate ever. When Monica tells Rachel, she mistakenly thinks the three of them are going to live together and is really excited about it, but it drives Chandler crazy. When Monica finally manages to tell Rachel that she and Chandler want to live on their own, Rachel isn't upset at all. This upsets Monica, because she thinks she deserves at least a few tears. However, it turns out that Rachel isn't upset because she doesn't think they're going to go through with it; they also cancelled their wedding in Vegas. When Monica tells her that it really is gonna happen, and that she and Rachel really aren't going to be roommates anymore, Rachel becomes quite upset and cries, saying it's the end of an era.
Moments later, Ross walks in, wanting to tell Rachel about the marriage, but she's really upset about moving out, and Ross instead hugs Rachel to comfort her. However, as he hugs her he realizes that, despite his protests to the contrary, he really is in love with her.