There are plenty of cars you can find for less than 6K
of course you will not find new or luxurious or performance cars, How good cars at that price come to mind, Alfa Romeo Mito, Volkswagen Golf or Polo, Ford Fiesta (or at least in Italy these are good cars less than 6k, if you live outside Europe then it's another world) anyway try to take cars that have less than 100,000km because if they have more than those kilometers maintenances may be required and some are very expensive, When you go to buy a car bring an experienced friend with you, he will be able to tell you if it is worth it or not (DON'T DECIDE TO BUY A CAR JUST BY LOOKING AT IT FROM ONLINE SITES)