Puzzle #237: Number Categories 2

The numbers two and six have a certain property. The numbers zero, one, three, four, five, seven, eight, and nine do not have this property. What is this property? [Hint: It has to do with the English spelling of each of the words.]

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, December 20, 2017 at noon Pacific Time. I will post the answer shortly after.