**Core Concept**
The clinical presentation of unilateral proptosis with bilateral sixth nerve palsy suggests a complex neuro-ophthalmological condition, likely involving the cavernous sinus or orbital apex. This combination of symptoms can be associated with **cavernous sinus thrombosis** or **orbital apex syndrome**, which are medical emergencies. The **sixth cranial nerve**, responsible for lateral rectus muscle function, is affected bilaterally, indicating a lesion or process that impacts both nerves, possibly at the level of the cavernous sinus.

**Why the Correct Answer is Right**
Given the symptoms, the most plausible explanation is a condition that affects the cavernous sinus, where both sixth nerves are closely approximated and can be simultaneously affected. **Cavernous sinus thrombosis** is a severe condition that can lead to these symptoms by causing venous congestion and subsequent swelling, which can compress the nerves passing through or near the cavernous sinus. The proptosis is typically unilateral, corresponding to the side of the primary pathology.

**Why Each Wrong Option is Incorrect**
**Option A:** This choice is incorrect because it does not account for the bilateral sixth nerve palsy in the context of unilateral proptosis.
**Option B:** Similarly, this option does not provide a satisfactory explanation for the combination of symptoms presented.
**Option C:** This choice is also incorrect as it fails to consider the neuroanatomical correlation necessary to explain bilateral sixth nerve palsy with unilateral proptosis.
**Option D:** Without specific details on Option D, we cannot directly address its inaccuracies, but given the clinical scenario, any option not considering cavernous sinus pathology or a similar process affecting both sixth nerves and causing proptosis would be incorrect.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that bilateral sixth nerve palsy can be a sign of increased intracranial pressure or a mass lesion affecting the brainstem or cavernous sinus, and when combined with unilateral proptosis, it strongly suggests a cavernous sinus syndrome. Prompt diagnosis and treatment are crucial to prevent serious complications.

**Correct Answer:** D. Cavernous sinus thrombosis.