Any solution we propose for how people live must be in their enlightened self interest. Call it whatever you will, but our current society is about blind consumption and short term thinking. It's pretty shit and could be much better.

I feel like the people arguing here, are mostly arguing over terms than real substantive differences.

https://en.wikipedia.org/wiki/Issues_in_anarchism#Definitional_concerns

For how socialism could be achieved through markets:

http://opensourceecology.org/wiki/Practical_Post-Scarcity_Video

https://en.wikipedia.org/wiki/Free-market_anarchism#Left-wing_market_anarchism

This left-right thing is nonsense anyway, I don't even believe in it.

https://en.wikipedia.org/wiki/Post-left_anarchy

As an ideal anarcho-capitalism is just as utopic as anarcho-communism. I've never heard a good answer as to who enforces property ownership. It's worth understanding that ownership of land (on which we were all born and belonged to nobody) is a purely western concept. Property is connected to labour- you might own the building, but you cannot own property titles to unused land without an enforcer/mafia.