The word 'heard' indicates that the statement is in the past tense and so the answer must be in the past tense. Further, the action in the sentence must be completed and not ongoing since the subject has already heard about it in the news.
Option A is incorrect. 'were being injured' is in the past tense but, 'being injured' indicates that the action is ongoing and not complete. Thus, it cannot be the answer.
Option B is incorrect. 'had injured' is in the past tense and indicates a complete action but, the sentence indicates that the family was in an explosion. Thus, it is the family that was injured. Using 'had injured' indicates that the family did the injuring, which is not the case. Further, using 'had injured' will require an object who was injured. Since there is no such object, 'had injured' cannot be used.
Option C is incorrect. 'have injured' is in the present tense. Since the tense of the sentence is past tense, the use of 'have injured' will make the tense of the sentence inconsistent.
Option D is correct. 'had been injured' is in the past tense. Also, it indicates that the action has been completed. Further, it also indicates that it was the family that was injured in the explosion as required by the sentence. Thus, it meets all the required conditions and is the correct answer.