**Core Concept**
The patient's presentation of sudden loss of right-sided motor function in the face, arm, and leg suggests a unilateral cerebral infarction, specifically a stroke. The involvement of the motor cortex, responsible for voluntary movement, is a key feature of this condition.

**Why the Correct Answer is Right**
The correct structure involved in this patient's injury is the **middle cerebral artery (MCA)**. The MCA is the largest cerebral artery and supplies a significant portion of the lateral surface of the brain, including the motor cortex, primary sensory cortex, and parts of the frontal and parietal lobes. The MCA is also a common site for occlusive thrombosis or embolism, leading to a stroke. In this patient, the recent initiation of Coumadin for atrial fibrillation increases the risk of thrombosis.

**Why Each Wrong Option is Incorrect**
**Option A:** The **anterior cerebral artery (ACA)** primarily supplies the medial surface of the brain, including the motor cortex for the lower limbs. While it can be involved in stroke, it is less likely to cause a contralateral face and arm deficit.
**Option B:** The **posterior cerebral artery (PCA)** primarily supplies the occipital lobe and the medial and lateral aspects of the temporal lobe. It is less commonly involved in stroke and is not typically associated with motor deficits.
**Option C:** The **basilar artery** supplies the brainstem, cerebellum, and posterior inferior cerebellar arteries. While it can be involved in stroke, it is less likely to cause a unilateral motor deficit in the face, arm, and leg.

**Clinical Pearl / High-Yield Fact**
In patients with atrial fibrillation, the risk of stroke is increased, and the use of anticoagulants like Coumadin is a common strategy to prevent thrombosis. However, patients on anticoagulants are at increased risk of intracranial hemorrhage if they experience a fall or trauma.

**Correct Answer:** C.