Why don't you ___ an example?

The correct choice is "cite" because it means to refer to or quote an example or piece of evidence, particularly in academic or formal contexts. In the sentence, the phrase "Why don't you ___ an example?" suggests that the speaker is asking someone to provide or mention a specific instance to illustrate a point.

The other options do not fit the context of the sentence. "Sighte" is not a recognized word in English, thus it cannot be a valid choice. "Site," while a real word, typically refers to a location or place, which does not align with the idea of providing an example. "Zite" is also not a standard English word and lacks relevance in this context. Therefore, "cite" is the only appropriate verb that correctly completes the sentence, maintaining the intended meaning.