What evidence supports the hypothesis that Earth is 4.6 billion years?

Among other things, rocks have been found that are over 4 billion years old. The age of such rocks is determined by radioactive dating. Note that this is not "a" method, but perhaps 40 different methods (depending on the isotopes involved), which complement one another.
The exact age of the Earth is harder to determine exactly; but basically, it must be at least as old as the oldest rocks found.