Question

what actions does ahineev take in order to protect his reputation?

Answer 1

Ahineev went around telling all the guests that he didn't kiss Marfa and tried his best to make sure that everyone knew that he didn't kiss Marfa.

Plot background of Anton Chekhov's "A Slender": Ahineev is mortified that Vankin would think he was kissing the cook, and anticipates that he will be spreading that story to the guests.  Determined to prevent such a slander, Ahineev makes the rounds of the party, telling everyone he can that there was nothing to the story Vankin would be spreading about him kissing Marfa in the kitchen.  In the process, he describes both Vankin and Marfa in the most unflattering terms, calling him a silly fool, and her a perfect fright whom no one would care to kiss.