**Core Concept**
A supracondylar fracture of the humerus is a common elbow fracture in children, typically occurring when a child falls onto an outstretched hand. The fracture occurs just above the condyles of the humerus, at the elbow joint. The displacement and angulation of the fracture fragments can lead to various deformities.

**Why the Correct Answer is Right**
The most common deformity seen in supracondylar fractures of the humerus is cubitus varus, also known as a "gunstock" deformity. This occurs when the distal fragment is displaced radially and posteriorly, resulting in a varus angulation of the elbow. This deformity can be due to the displacement of the fracture fragments during the injury or due to the pull of the triceps tendon on the distal fragment. The cubitus varus deformity can be a cosmetic concern and may also lead to functional impairment.

**Why Each Wrong Option is Incorrect**
* **Option A:** Cubitus valgus is a less common deformity seen in supracondylar fractures, where the distal fragment is displaced ulnarly and anteriorly, resulting in a valgus angulation of the elbow. This is not the most common deformity.
* **Option B:** Posteromedial displacement of the distal fragment is not a typical deformity seen in supracondylar fractures. This type of displacement would result in a different type of deformity.
* **Option D:** Hyperextension of the elbow is not a deformity seen in supracondylar fractures. Supracondylar fractures typically result in flexion of the elbow.

**Clinical Pearl / High-Yield Fact**
The "three Ps" of supracondylar fractures are: posterior displacement, posterior angulation, and posterior comminution. These factors can contribute to the severity of the deformity and the complexity of the fracture.

**Correct Answer:** C.