There was a lot of private property in the socialist countries. I am not sure from where this thought even came to you. What was impossible was owning big private enterprise. But small businesses - like a restaurant or a shoe repair shop were allowed. You were also allowed to own houses, cars, appliances, clothes and almost everything else. Land was a bit weird - you could own, but not too much - basically stuff that was small enough to evade the collectivisation process.