On the further assumption that the multiverse is infinite, which is plausible, all combinations of things that physically could co-occur do co-occur. For example, there are universes within this cosmos in which you are not reading this post but in which everything else is more or less the way it actually is. So, we can treat the universes in cosmos as physically possible worlds. Given the magnitude of infinity all physically possible combinations are instantiated somewhere. There may also be parallel universes that did not originate in the Big Bang of our multiverse. But we can set those aside here.
Here is the core of Greene's skeptical argument. Some of the universes in the cosmos will involve computer simulations similar to the one outlined in the movie The Matrix, except the simulations would not need to be global events. In a single universe with beings like us there could be a vast number of local simulations. So, if we ask whether it is more likely that reality is more or less as we experience it or that I am in a simulation, the answer is the latter. For each universe that have beings like us in them, many simulated universes can be created. So, it is likely that there are more simulated universes with beings like us than real, non-simulated universes with beings like us. This makes it more likely that reality is a simulation than that it is as we experience it. Of course, mere likelihood does not add up to justification. But the likelihood appears to undermine any justification we might have for thinking that we are not in simulation. So, it would seem that most of our beliefs about the world fail to be justified.
But this seems to generate some problems for Greene's argument. He thinks that we are justified in believing that the standard model of physics is correct, that the universe is expanding, that the universe originated in a Big Bang, etc. But if his argument is correct, then we are not justified in believing this. Hence, we are not justified in believing the premises of his argument.
For all we have said, Greene's argument could still be sound, as the premises could be true, even if we are not justified in believing them. But here is the thing. If it's likely that our reality is a simulation, then it is also likely that the standard model of physics does not obtain. There is no reason that all the real laws of physics should be preserved in a simulation. So, Greene has in effect shown that if the standard model of physics, together with certain other hypotheses, are correct, then they are likely incorrect. His theory appears to be self-undermining.