Option 1 -> Starts with "in their quest" which cannot begin a sentence without a subject.
Option 2 -> Forms a complete sentence: "Many people give a free rein to enthusiasm in their quest to entertain forgetting that the first quality of a critical work is to be accurate, and the second to be interesting" - logical flow with proper subject-verb-object structure.
Option 3 -> Begins with "is to be accurate" which lacks a subject and creates a fragment.
Option 4 -> Places (B) immediately after (D), creating "enthusiasm is to be accurate" which is grammatically incorrect.
Hence, Option 2: (D), (A), (C), (B) -> The sentence flows naturally with (D) establishing the main subject and verb, (A) providing the reason, (C) introducing what is forgotten, and (B) completing the thought about the two qualities of critical work -> correct