The song was being listened to by the children carefully.
The object of the verb in the active voice becomes the subject in the passive voice. i.e. The words, 'the song' becomes the singular subject in the passive voice. As the sentence is in past continuous tense, the auxiliary verb 'was being' is to be used along in the passive voice. The past participle form of the main verb (listened) is to be used. As the sentence in active voice has the preposition, 'to' following the verb, the verb in the passive voice should also be followed by the same preposition.
Option A is incorrect as the continuous form of the verb i.e 'listening' should not be used in the passive voice. The past participle form of the verb i.e 'listened' has to be used.
Option B: Here, the correct form of the verb i.e 'was being listened' is used. However, the verb has to be followed by the preposition 'to', which is missing. Hence, this option is incorrect.
Option C: Here, the words 'The song' is the subject. The auxiliary 'was being' is used along with the singular subject. The past participle form of the verb (listened) is used along with the preposition, 'to'. Hence, this option is correct.
Option D is incorrect as option C is the correct answer.