(A) Put one's shoulder to the wheel = (I) Work hard at a task ✓
(B) Throw down the gauntlet = (II) Take up a challenge ✓
(C) Get too big for one's boots = (IV) Become very conceited ✓
(D) Cut one's coat according to one's cloth = (III) Spend within the limits of what one can afford ✓
Hence, Option 3: (A) - (I), (B) - (II), (C) - (IV), (D) - (III) -> "Put one's shoulder to the wheel" means to work hard and make a strong effort; "Throw down the gauntlet" means to issue or accept a challenge; "Get too big for one's boots" means to become conceited or arrogant; and "Cut one's coat according to one's cloth" means to live within one's means and spend only what one can afford -> correct