**Core Concept**
The question is testing the understanding of the regulatory mechanisms controlling glycogenolysis and gluconeogenesis, particularly the role of glucagon and insulin in these processes. Glucagon and insulin are two key hormones that regulate glucose metabolism, with glucagon promoting gluconeogenesis and glycogenolysis and insulin inhibiting these processes.

**Why the Correct Answer is Right**
Phosphoenolpyruvate carboxykinase (PEPCK) is a key enzyme involved in the gluconeogenic pathway. Glucagon stimulates the activity of PEPCK by increasing its gene expression and protein synthesis. In low insulin/glucagon ratio, the activity of PEPCK is increased, leading to an increase in gluconeogenesis. This is a critical adaptation to maintain blood glucose levels during fasting or starvation.

**Why Each Wrong Option is Incorrect**
* **Option A:** Glucose-6-phosphatase is an enzyme involved in the final step of gluconeogenesis and glycogenolysis. Its activity is indeed increased in low insulin/glucagon levels, but it is not the primary enzyme regulated in this context.
* **Option B:** Glycogen synthase is an enzyme involved in glycogen synthesis, which is inhibited by low insulin/glucagon levels. Its activity is not increased in low insulin/glucagon ratio.
* **Option D:** Pyruvate kinase is an enzyme involved in glycolysis, which is inhibited by high glucagon levels. Its activity is not increased in low insulin/glucagon ratio.

**Clinical Pearl / High-Yield Fact**
A key clinical correlation is that glucagon-like peptide-1 (GLP-1) analogs, used in the treatment of type 2 diabetes, can inhibit glucagon secretion and increase insulin secretion, thus reducing glucose production in the liver.

**Correct Answer: C. Phosphoenolpyruvate carboxykinase (PEPCK) is increased in low insulin/glucagon level.**