**Core Concept:**
The question refers to a specific type of congenital hand deformity characterized by abnormal joint positioning. In this case, we need to identify the joint combination where one joint is flexed and another is extended. In the context of fingers, there are three types of interphalangeal joints: distal interphalangeal (DIP), middle interphalangeal (PIP), and proximal interphalangeal (PIP) joints.

**Why the Correct Answer is Right:**
The correct answer, **C. Hallux Valgus** is the deformity where the DIP joint is flexed, and the PIP joint is extended. Hallux valgus is a common foot deformity affecting the big toe, where the big toe moves towards the second toe, causing the first metatarsal head to deviate laterally and the first and second metatarsophalangeal joints to deviate medially. This results in the DIP joint flexion and PIP joint extension.

**Why Each Wrong Option is Incorrect:**
A. Hallux Rigidus (DIP joint arthrosis) - In this condition, the DIP joint is stiff and immobile due to degenerative changes, not flexion.
B. Hallux Abductus (abduction of the first ray) - This is a different deformity involving the abduction of the first ray (first metatarsal and phalangeal bones), not the flexion of the DIP joint and extension of the PIP joint.
D. Hallux Valgus (flexion of PIP joint and extension of DIP joint) - This is the correct answer, so there is no need to elaborate on this option.

**Clinical Pearl:**
Hallux Valgus is a common foot deformity caused by the imbalance of forces acting on the first ray, resulting from inherited or acquired factors. It can lead to pain, discomfort, and difficulty in wearing shoes. Early recognition and intervention may prevent worsening of the deformity and improve the patient's quality of life.

**Correct Answer:** C. Hallux Valgus