weeeell..
one point- radiocarbon dating assumes the old theory of the same rate of growth we see now or decay now.. is the same all through history. So.. you get a mountain growing at a rate of half an inch a year.. and then multiply it back wards to reach the total height of the mountain and you get tons and tons of time.
This assumption does not acknowledge catastrophe, with rapid burials induced by things like earthquakes, tsunamis, floods etc..
There are many areas of coal in hillsides with fossilised trees running through there layers, in a state that has to be quick burial. The same goes for tons and tons of fossilised fish around the world, where they were caught in a state of movement.. quickly buried. Now I do not know exaclty which areas have these characteristics.. but I do know their are areas that people have just looked and assumed are millions or billions of years old.. with these fossilised trees going thru their layers.
Also have a look at the fossils in the Smithsonian museum on display.. it has complete skeletons preserved .. how is that so? You really only get this with quick burial.
So you may say.. okay they were buried quick but then the layers that fell on them after were slow. Well this doesn't hurt young earth theory at all! If they get buried quick.. they still get thousands of years to be buried with more sediment!
The right assumption with ages of things.. is to factor in catastrophic occurences.. which I am sure up to date evolutionists do now.. but what I have heard they are now finding is that there own updated theory is getting closer and closer now to creationist young earth explanations.
Anyhoo.. after all that.. 6,000-10,000 years for me..