The correct option is (D), (A), (C), (B).

Let us break down the sentence construction step-by-step to understand why this sequence is correct:

1. Identifying the Subject and Initiating Action (D):
The phrase (D) "she worked on the case" contains the main subject ("she") and the verb ("worked"). It serves as the most natural starting point of the sentence, establishing the actor and the action.

2. Adding Duration and Transition (A):
The phrase (A) "for seven hours but was hardly" connects directly to the action in (D). It describes the duration of her work ("for seven hours") and introduces a contrast using the conjunction "but" followed by the modifier "was hardly".

3. Completing the Description of the Struggle (C):
The adverb "hardly" in (A) requires an adjective to complete its meaning. The phrase (C) "able to decide who the murderer was" starts with the adjective "able", which perfectly completes the phrase to read "was hardly able to decide...". This expresses what she was struggling to achieve.

4. Providing the Reason or Cause (B):
The phrase (B) "because of the absence of any motivation" uses the prepositional phrase "because of" to explain the reason behind her struggle, bringing a logical conclusion to the sentence.

Combining these parts in the sequence (D) → (A) → (C) → (B) forms a grammatically correct and coherent sentence:
"She worked on the case for seven hours but was hardly able to decide who the murderer was because of the absence of any motivation."