Thanks for your question. I think the others have done a good job of answering it. It depends if the whole sentence is using "honest" correctly as an adjective. I don't have the entire sentence, so it's hard for me to say. For example, to show his honest opinion to show his honest bearing to show his honest way of doing things The examples above are all acceptable ways to use the adjective "honest." But, if you need the noun form with the infinitive as in these phrases: To show respect To show thoughtfulness To show caution and prudence then, you need the noun form of the adjective "honest." "Honesty" is the noun form. To show honesty and integrity and righteousness Or if you want to use the adjective, you can substitute a noun clause for the word "honesty." He has to show that he is honest. He has to show that he's an honest person. I hope that was my honest answer for you.

Honest is an adjective. You need a noun. Honesty. Show somebody's noun is a fine pattern "Show your true colors" is an expression. Some examples: Show them the book Show off your car

to show his honesty.

To answer the question in the title - the phrase is correct, but it doesn't mean what you think it does. In "to show somebody's + a noun", the 's is short for "is". It doesn't indicate possession here.

Is that the full phrase? Then it should read "...to show his honesty". Perhaps there's a noun which follows "honest", such as "to show his honest intentions". Alternately, the phrase could be badly-written, and should read "to show he's honest".