**Core Concept**
The patient's inability to speak but ability to understand speech suggests a lesion in the area of the brain responsible for expressive language, but not comprehension. This is a classic symptom of Broca's aphasia, which is associated with damage to the left frontal lobe, specifically the Broca's area.

**Why the Correct Answer is Right**
The Broca's area is located in the inferior frontal gyrus (Brodmann areas 44 and 45) of the left hemisphere. It is responsible for speech production, articulation, and grammar. Damage to this area, often as a result of stroke or traumatic brain injury, leads to Broca's aphasia, characterized by non-fluent, effortful speech with difficulty finding words and articulating them correctly. The patient's ability to understand speech, but not produce it, is known as anomic aphasia, which is a type of aphasia where the patient has difficulty recalling the names of objects, people, and places.

**Why Each Wrong Option is Incorrect**
**Option A:** Wernicke's area is involved in speech comprehension and is located in the left posterior superior temporal gyrus. Damage to this area leads to Wernicke's aphasia, characterized by fluent, but meaningless speech. This is not consistent with the patient's symptoms.

**Option B:** The primary motor cortex is responsible for motor functions, including facial movements and articulation. However, damage to this area would result in weakness or paralysis of the face and limbs, which is not described in the scenario.

**Option C:** The primary sensory cortex is responsible for processing sensory information, including touch and proprioception. Damage to this area would result in sensory deficits, such as numbness or loss of proprioception, which is not consistent with the patient's symptoms.

**Option D:** The basal ganglia are involved in motor control and cognition. However, damage to this area would result in movement disorders, such as Parkinson's disease, or cognitive deficits, such as dementia, which is not consistent with the patient's symptoms.

**Clinical Pearl / High-Yield Fact**
The classic sign of Broca's aphasia is the patient's inability to say "pardon?" or "what?" when they do not understand a question, even though they may be able to nod or shake their head to indicate understanding.

**Correct Answer:** C.