**Core Concept**
The patient's symptoms and radiographic findings suggest a specific type of fracture involving the distal radius. This fracture is a common injury seen in patients with a fall onto an outstretched hand, resulting in a displacement of the distal fragment.

**Why the Correct Answer is Right**
The most likely fracture involved in this case is a **Colles' fracture**. This type of fracture occurs when the distal radius is displaced posteriorly due to a fall onto an outstretched hand. The distal fragment is displaced in a dorsal direction, resulting in a characteristic "dinner fork" deformity. The fracture occurs at the level of the distal radius, typically between the radiocarpal joint and the distal radioulnar joint.

**Why Each Wrong Option is Incorrect**
* **Option A:** A **Smith's fracture** is a type of fracture where the distal fragment is displaced in a volar (palmar) direction, which is opposite to the direction seen in a Colles' fracture.
* **Option B:** A **Galeazzi fracture** is a type of fracture that involves the distal radius and the distal radioulnar joint, but it is not characterized by a posterior displacement of the distal fragment.
* **Option D:** A **scaphoid fracture** is a type of fracture that occurs at the scaphoid bone, which is one of the carpal bones in the wrist. While it can occur after a fall onto an outstretched hand, it is not typically associated with a posterior displacement of the distal wrist and hand.

**Clinical Pearl / High-Yield Fact**
It's essential to note that a Colles' fracture can be associated with other injuries, such as a scaphoid fracture or a distal radioulnar joint injury. A thorough examination and imaging studies are necessary to rule out these associated injuries.

**Correct Answer: C. Colles' fracture**