He starts out with an explanation of what carbon dating is, which proves to be adequate for this discussion.The only notable exception is that he says carbon dating is only good for objects less than 40,000 years old. As technologies advance, so does our ability to detect the amount of C-14 in a sample.
Some organic materials do give radiocarbon ages in excess of 50,000 "radiocarbon years." However, it is important to distinguish between "radiocarbon years" and calendar years.
Beyond that timespan, the amount of the original C formed by irradiation of nitrogen by neutrons from the spontaneous fission of uranium, present in trace quantities almost everywhere.
For these samples, other dating methods must be used.
Other radiometric dating methods such as potassium-argon or rubidium-strontium are used for such purposes by those who believe that the earth is billions of years old.
Radiocarbon is not suitable for this purpose because it is only applicable: a) on a time scale of thousands of years and b) to remains of once-living organisms (with minor exceptions, from which rocks are excluded).