**Core Concept**
The underlying principle being tested is the metabolic pathways of glycogenolysis and glycogenesis, focusing on the enzymes involved in these processes. Glycogenolysis is the breakdown of glycogen to glucose, while glycogenesis is the synthesis of glycogen from glucose.

**Why the Correct Answer is Right**
The correct answer is related to the enzyme that participates in both the breakdown and synthesis of glycogen. This enzyme is crucial for the interconversion of glucose-1-phosphate and glucose-6-phosphate, a step common to both glycogenolysis and glycogenesis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it refers to an enzyme specific to glycogenolysis.
**Option B:** This option is also incorrect as it is involved in a different step of glycogen metabolism.
**Option D:** Similarly, this option is incorrect because it participates in glycogenesis but not in the common step with glycogenolysis.

**Clinical Pearl / High-Yield Fact**
The enzyme phosphoglucomutase is key to both glycogenolysis and glycogenesis, facilitating the interconversion between glucose-1-phosphate and glucose-6-phosphate.

**Correct Answer:** C. Phosphoglucomutase.