Final answer:
The instance of persuasive speaking in the provided options is a Debate arguing a point of view, where the aim is to influence the audience's thoughts or actions.
Step-by-step explanation:
An instance of persuasive speaking is characterized by the speaker trying to convince the audience of something, influencing their beliefs, values, or behavior. The correct answer among the choices provided is a Debate arguing a point of view, as this directly involves persuading or influencing an audience to support a particular stance on a topic. In contrast to informative speech, which aims to present clear and direct information without necessarily swaying the audience's viewpoint, or an entertaining speech which is primarily for enjoyment, persuasive speech involves presenting a viewpoint, supporting it with reasoning and evidence, and addressing counterclaims. This is all done with the intention of changing or reinforcing the audience's existing beliefs or actions.