The correct answer is B. The instructions were being read out by the invigilator.
The other options are incorrect because they do not accurately reflect the tense of the sentence. Option A, The instructions were read by the invigilator, is in the past tense, but the sentence is in the present tense. Option C, The instructions had been read out by the invigilator, is in the past perfect tense, but the sentence does not indicate that the instructions have been read. Option D, The instructions had been read by the invigilator, is also in the past perfect tense, but it does not indicate that the instructions were being read.
The sentence The invigilator was reading out the instructions indicates that the invigilator was in the process of reading the instructions. This is consistent with the use of the present progressive tense.