Rachel Green's second birthday party happened in the Season 9 episode "The One With Phoebe's Rats".

At the party, Rachel was worried about her new colleague Gavin Mitchell which Monica did.

Chandler tried to stop Joey from trying to make a move on Emma's new nanny Molly, under Ross's request.

Only later, Gavin turned up at the party after everyone left and kissed Rachel and she kissed him back, something which Ross saw from his apartment.