**Core Concept**
The child's inability to utilize glucose from glycogenolysis or gluconeogenesis suggests a defect in the pathways that regulate glucose production in the liver. This condition is associated with a deficiency in an enzyme that catalyzes a critical step in these pathways.

**Why the Correct Answer is Right**
The enzyme responsible for catalyzing the conversion of fructose-1,6-bisphosphate to fructose-6-phosphate in the gluconeogenic pathway is phosph-fructokinase-2 (PFK-2). However, the question is likely referring to a deficiency in the enzyme that catalyzes the conversion of glucose-6-phosphate to glucose, which is necessary for gluconeogenesis and glycogenolysis. This enzyme is glucose-6-phosphatase (G6Pase). The deficiency of G6Pase leads to von Gierke's disease, a type of glycogen storage disease characterized by hypoglycemia and lactic acidosis.

**Why Each Wrong Option is Incorrect**
* **Option A:** Debranching enzyme deficiency leads to Cori's disease, which primarily affects glycogen breakdown in muscles.
* **Option B:** Phosphorylase kinase deficiency affects glycogen breakdown in muscles and liver, but does not impair gluconeogenesis.
* **Option C:** Glucose-6-phosphate dehydrogenase (G6PD) deficiency is associated with hemolytic anemia, not hypoglycemia.

**Clinical Pearl / High-Yield Fact**
Glucose-6-phosphatase deficiency (von Gierke's disease) is a classic example of a glycogen storage disease that affects glucose production in the liver, leading to severe hypoglycemia and lactic acidosis.

**Correct Answer:** D. Glucose-6-phosphatase.