it happened when the 4th great ninja war happened and they reveled who was behind the mask(Tobi). Obito survived and then was going to keep going on with project(ultimate genjustu).Kakashi asked why he is working with Madara and said it was because he let Rin die. Then they went into the past and Obito survived because Madara(who was vey old at that time) saved him.Since the entire right side of his body was demolished it was replaced with some of Harashrama's wood thing. Zetsu was in it too but only the right side and along with a swirly faced guy just like him. Madara had a conversation with him saying that since he saved him he will do as he says. He kept refusing and Zetsu and the other guy helped him get at least a bit stronger, or until he could walk. He was determined to because he wanted to see Kakashi and Rin again. Obito told Zetsu to keep an eye on them. So he did until he sensed that they were in a spike. Obito tryed to get out by punching the huge boulder out but instead he ended up huring his arm. So the Swirly guy wrapped around Obito like a cloak and Obito tried again. So he ran and then the eye that was still with him saw Rin with something peirced on the left side of her chest. He didn't belive it until he got to where Kakashi and Rin were. Kakashi used his Chidori and killed Rin with it. He was too injured and by the time he fainted he got his mangekyo awakened. He colapsed. Since Obito had the same eye as Kakashi, he was also able to use the mangekyo.The ninja who were attacking Rin and Kakashi were from the mist.Obito killed them all and left. One of them said they should still take Rin's body since it had too much information. So Kakashi killed Rin because of that or Rin said to do it.