Can anyone explain to me how they can determine that the bones are 9300 years old, when carbin dating is only good to 6000 years.
Where'd you hear that?
50,000 years is the accepted figure for Carbon 12/nitrogen-14 dating.
Someone's been feeding you a story. C-14 dating gets a bit iffy about 50000 years down the line, but 6000? That's just over one half-life, can not only get a good reading, but it's within the tree-ring correction calibration area.
You are confusing the half life of carbon 14 with the effective dating range. While the half life is about 5700 years, the ability to measure trace amounts allows dating to extend to the range of 50,000 years with the C-14 process.
As ElkGroveDan said, the half-life of C14 makes the dating possible, and with the enhancements to sensitivity of the instrumentation used, the upper limit for dating is now about 60,000 years. Further enhancements may push that limit a bit more.