First, there are quite a few "How do you stop [x, y, or z] in an Anarchist society" questions on this site, and they may be helpful in thinking through the premises and possibilities. I don't feel like rehashing that here, though someone else may. Here's a sampling:
Second, as to capitalism specifically, arguably capitalism is impossible in an anarchist society, if the terms are properly defined. Capitalism relies on the state to the extent that state forces are what keep people in (or returning to) capitalist relations. For example, the reality or threat of police violence, imprisonment, and other coercive measures keep people from subverting, abandoning and destroying capitalist means of relating. (There is a sidebar here about people's willingness or even desire to participate in their own subordination, which I will leave for another time/place, and not because I don't think it's valid!) This has been argued before on the site, including here:
With this understanding, we would see that "anarcho-capitalism" is not really anarchist in the sense that it relies on police and prisons which, even if they are privatized, are not substantially less statist than other means of social control.
It is probably clear how this all relates to your question. It is entirely possible, if we reject the idea of Anarchist Social Revolutionary Totality, for anarchist groupings to inhabit a world that is also inhabited by capitalist groupings. Well, that is the reality today, but we could also, as outlined in Desert, see a shift of power and a slippage in social control that would allow anarchists and others to have more regions of autonomy than are present today, but without a total annihilation of capitalism. In that scenario, there are a lot of ways the capitalist hubs could be hindered, deserted, weakened, destroyed, and so on, as influenced by the limits and possibilities and ingenuities of the situation. I just don't think there is any way to say "This is how capitalism would be stopped" in a generalized hypothetical world, and moreover it is a game I do not want to play, as it asks the argument to step into the realm of more-or-less state policy, or pretending to be 'anarchist' generals, politicians and bureaucrats.