**Core Concept**
The patient's presentation of diplopia on seeing towards the left side in the context of chronic suppurative otitis media (CSOM) suggests a possible lesion affecting the abducens nerve (CN VI), which is responsible for lateral rectus muscle function and horizontal eye movement.

**Why the Correct Answer is Right**
The abducens nerve (CN VI) is a cranial nerve that emerges from the brainstem and passes close to the petrous part of the temporal bone, which is frequently involved in CSOM. Inflammation or infection in the petrous apex can lead to nerve compression or damage, resulting in weakness or paralysis of the lateral rectus muscle, causing diplopia on looking towards the affected side. This clinical scenario is a classic presentation of abducens nerve palsy secondary to petrous apex syndrome.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not directly related to the clinical scenario of CSOM and diplopia. While facial nerve palsy is a common complication of CSOM, it does not typically present with diplopia.

**Option B:** This option is incorrect because the trochlear nerve (CN IV) controls the superior oblique muscle, which is primarily responsible for intorsion and depression of the eyeball. Damage to the trochlear nerve would not cause diplopia on looking towards the left side.

**Option C:** This option is incorrect because the oculomotor nerve (CN III) controls multiple extraocular muscles, including the medial rectus, inferior rectus, and inferior oblique. While damage to the oculomotor nerve can cause diplopia, it would not be limited to looking towards the left side.

**Clinical Pearl / High-Yield Fact**
In cases of CSOM, look for signs of cranial nerve involvement, particularly the abducens nerve (CN VI), as petrous apex syndrome can cause a range of neurological symptoms, including diplopia, facial numbness, and hearing loss.

**Correct Answer: B. Abducens nerve palsy secondary to petrous apex syndrome.**