**Core Concept**
Thrombosis in cerebral vessels can lead to hemiplegia due to the interruption of blood flow to the brain's motor cortex, resulting in damage to the corticospinal tract. The corticospinal tract is a critical pathway for motor control, and damage to this tract can cause hemiplegia, characterized by weakness or paralysis of one side of the body.

**Why the Correct Answer is Right**
The correct answer is likely related to the middle cerebral artery (MCA), which is the largest cerebral artery and supplies a significant portion of the brain's motor cortex. Thrombosis of the MCA can lead to damage to the M1 segment, which is responsible for supplying the motor cortex. This damage can cause hemiplegia due to the interruption of blood flow to the motor cortex. The MCA also supplies the precentral gyrus, which is the primary motor cortex responsible for voluntary movements.

**Why Each Wrong Option is Incorrect**
* **Option A:** Thrombosis of the posterior cerebral artery (PCA) would more likely cause visual field defects, memory disturbances, and other non-motor symptoms due to its supply to the occipital lobe, temporal lobe, and thalamus.
* **Option B:** Thrombosis of the anterior cerebral artery (ACA) would more likely cause weakness or paralysis of the lower limbs due to its supply to the medial surface of the hemisphere, including the precentral gyrus for the lower limbs.
* **Option C:** Thrombosis of the basilar artery would more likely cause brainstem symptoms, including cranial nerve deficits, ataxia, and long tract signs due to its supply to the brainstem and posterior circulation.

**Clinical Pearl / High-Yield Fact**
The MCA is the most common site for cerebral infarction, accounting for approximately 50-60% of all ischemic strokes. Understanding the anatomy and vascular supply of the brain is crucial for diagnosing and managing stroke patients.

**Correct Answer: C**