When should you concede to a counterargument? when your audience believes the counterargument when it’s a controversial subject and you want to avoid hurt feelings when you discover that the counterargument is a logical fallacy when the counterargument has a relevant point

The final choice, "when the counterargument has a relevant point," is correct.

to rule the other ones out:
just because your audience believes in a point, doesn't mean you should give in. you could still be correct and you shouldn't be swayed by the beliefs of your audience.

in an argument, controversy and hurt feelings usually arise regardless. ideally, you wouldn't concern yourself w it

if the counterargument is a "logical fallacy," that means that the counterargument sounds very logical and convincing, but it's actually invalid. not choosing this answer choice basically depends on your knowledge of the word "fallacy."