"Make/do/take/run/keep/give a laugh" — which one makes sense?
I believe they're looking for give a laugh.
Though I wouldn't use that phrase by itself, I've frequently seen usages like "he gave a hearty laugh."
I agree with the two previous posters that only ‘give’ comes close.
One the teacher might have inclued is ‘have’, as in
You’re ‘avin’ a larf, incha?
Something hilarious might 'give' you a laugh.