**Core Concept**
Refsum's disease is a rare genetic disorder characterized by the accumulation of a specific type of fatty acid in the body. This accumulation leads to a range of clinical symptoms, including peripheral neuropathy, retinitis pigmentosa, and cerebellar ataxia. The disease is caused by a deficiency in the enzyme responsible for breaking down a particular type of fatty acid.

**Why the Correct Answer is Right**
The correct answer is **phytanoyl-CoA hydroxylase**. This enzyme plays a crucial role in the breakdown of phytanic acid, a type of fatty acid that is normally converted into a more water-soluble compound and excreted from the body. In Refsum's disease, the deficiency of phytanoyl-CoA hydroxylase leads to the accumulation of phytanic acid in the body, causing the various clinical symptoms associated with the disease.

**Why Each Wrong Option is Incorrect**
**Option A:** Phytanoyl-CoA carboxylase is not directly involved in the breakdown of phytanic acid, but rather is an enzyme involved in the synthesis of fatty acids.
**Option B:** Alpha-hydroxy acid oxidase is involved in the breakdown of certain amino acids, but is not relevant to Refsum's disease.
**Option C:** 3-hydroxy-3-methylglutaryl-CoA (HMG-CoA) reductase is an enzyme involved in the synthesis of cholesterol, and is not related to Refsum's disease.

**Clinical Pearl / High-Yield Fact**
Refsum's disease is an example of a **metabolic disorder**, where a deficiency in a specific enzyme leads to the accumulation of a particular type of molecule in the body, causing clinical symptoms. This type of disorder is often diagnosed through a combination of clinical evaluation, laboratory tests, and genetic analysis.

**Correct Answer: C. Phytanoyl-CoA hydroxylase.**