Explanation:

The original sentence is incorrect

Reason: There are two errors in the bold part.

Firstly, the term ‘furniture’ is a collective noun. Collective nouns are used in singular form. Therefore, ‘furnitures’ must be replaced by ‘furniture’ in order to make the sentence correct.

Secondly, the word ‘family’ has been used in singular form and should be followed by a singular verb. Therefore, ‘were’ should be replaced by ‘was’ in order to make it a grammatically correct sentence.

Among the choices available, option C replaces the bold part most appropriately.

The sentence after replacement becomes:

The accumulated dust on the furniture indicated that the family was long gone.

Option C is hence the correct answer.