Option 1 -> Incorrectly matches "cool one's heels" with making fine distinctions and "bury the hatchet" with aimless talk.
Option 2 -> Incorrectly matches "cool one's heels" with aimless talk and "chew the cud" with waiting.
Option 3 -> Incorrectly matches "cool one's heels" with forgetting enmity and "bury the hatchet" with waiting.
Option 4 -> Correctly matches all idioms: "cool one's heels" means to wait; "bury the hatchet" means to forget enmity/make peace; "chew the cud" means to talk aimlessly; "split hairs" means to make overly fine distinctions.
Hence, Option 4: (A) - (II), (B) - (I), (C) - (IV), (D) - (III) -> The idioms are properly matched with their established meanings: cooling one's heels refers to waiting (often impatiently), burying the hatchet is about ending conflicts, chewing the cud means rambling conversation, and splitting hairs involves making petty distinctions -> correct