**Core Concept**
The patient's presentation of sudden onset left-sided hemiparesis, right-sided lower motor neuron (LMN) facial palsy, and inability to abduct the right eye suggests a lesion in the brainstem, specifically affecting the corticobulbar tract, the facial nerve, and the abducens nerve. This clinical scenario is a classic example of a brainstem stroke, where the specific combination of cranial nerve deficits and contralateral hemiparesis points towards a specific syndrome.

**Why the Correct Answer is Right**
Milion-Gubler syndrome is a brainstem stroke syndrome characterized by a lesion in the pons, resulting in a combination of ipsilateral (on the same side) lower motor neuron facial palsy and contralateral (opposite side) hemiparesis, along with impairment of the cranial nerves III, IV, and VI. This occurs due to the involvement of the corticobulbar tract, which carries motor fibers from the cerebral cortex to the cranial nerves, and the corticospinal tract, which carries motor fibers from the cerebral cortex to the spinal cord. The facial nerve is affected ipsilaterally due to its close proximity to the corticobulbar tract in the pons.

**Why Each Wrong Option is Incorrect**
**Option A:** Foville's syndrome typically presents with ipsilateral (on the same side) cranial nerve deficits, including the facial nerve, along with contralateral hemiparesis, but it also involves the medial longitudinal fasciculus (MLF), which is not the case in Milion-Gubler syndrome.
**Option C:** Ramsay Hunt syndrome is a viral infection affecting the facial nerve, causing ipsilateral facial palsy, but it does not explain the contralateral hemiparesis or the inability to abduct the eye.
**Option D:** Tolosa-Hunt syndrome is a painful ophthalmoplegia due to an inflammatory process affecting the cavernous sinus or superior orbital fissure, which does not account for the contralateral hemiparesis or the LMN facial palsy.

**Clinical Pearl / High-Yield Fact**
Milion-Gubler syndrome is a classic example of a brainstem stroke syndrome, and its recognition is crucial in the acute management of stroke patients. The combination of ipsilateral cranial nerve deficits and contralateral hemiparesis should prompt a thorough evaluation for a brainstem lesion.

**✓ Correct Answer: B. Milard Gubler syndrome**