Kakashi will destroy Obitos sharingan
Now with the title, I mean he will destroy the one in Obitos head :-)
I could see Kakashi giving up his life in order to destroy it, or at least letting Obito land a fatal blow on him that would make him injured too much for further participation in the war however, if Kakashi takes such a hit and destroys Obitos eye at the same time, he would make it easy for the rest of the shinobi to take him down, and Kakashi would have done the hardest part.
The way it happens can be in a countless of ways, but if Kakashi is going to die he has to say some last words to Naruto. Because of this I could see something entirely different happening.
Kakashi will be absorbed to Obitos dimension along with Obito, but as they arrive in the dimension, Kakashi manages to destroy Obitos sharingan, thus capturing both of them in the dimension. Naruto clone is there, and will be surprised, but he will also defend Kakashi, and be ready to take out Obito. Kakashi wants Naruto to wait, and they have a long talk. We get explanation about Rin. At the start obito wont care since he now thinks he has lost since he is stuck in his own dimension, but then Naruto uses talk no jutsu, obito goes good, Kakashi uses his last power to send obito out of the dimension, thus Kakashi will be stuck and die cause he has a fatal wound, and no chakra left. But he will be able to say goodbye to Naruto, since his clone is still there.
Perhaps you could say that Kakashi should also say goodbye to Sakura, since we all remember how Asuma said goodbye to his students. But Kakashi is of course a man of a few words. Who knows. Anyway there are a ton of possibilities, but my initial premise about Kakashi destroying Obitos eye, is what it is all about. Perhaps it will happen in the real dimension, and Kakashi will be saved by someone else, and Obito wont realize he is wrong until the moment of his death. I just don't see Kakashi actually beating Obito right now, unless they start talking about Rin, but that would also be the easy and too obvious choice I think. Anyway: