Final answer:
The most likely location of the lesion causing difficulty raising the right eyebrow, issues holding air in the right side of the mouth, and loss of hearing in the right ear is the right pontomedullary region.
Step-by-step explanation:
The symptoms described in the question suggest a lesion affecting the facial nerve, which controls the muscles of facial expression, including raising the eyebrow and holding air in the cheek, and the auditory nerve, responsible for hearing. This implies that the lesion is likely located in the right pontomedullary region (d), where these cranial nerves have nuclei or exit the brainstem. Lesions in this area can damage the nerves or their nuclei, leading to the clinical signs described. If a lesion were in the cerebral cortex, it would likely cause contralateral symptoms due to the crossing of neuronal pathways.