**Core Concept**
Jaundice in children can lead to various complications, including Wilson's disease, a genetic disorder affecting copper metabolism. The bluish pigmentation over the lunula, or the half-moon shaped area at the base of the fingernails, is a characteristic sign of this condition. Wilson's disease can cause neurological symptoms, including behavioral disturbances and difficulty in walking.

**Why the Correct Answer is Right**
The correct answer is B. Slit lamp examination because Wilson's disease often presents with Kayser-Fleischer rings, which are copper deposits in the cornea that can be visualized with a slit lamp. This is a critical diagnostic clue for Wilson's disease. The Kayser-Fleischer rings are a result of the accumulation of copper in the Descemet's membrane of the cornea, which can be detected by a slit lamp examination.

**Why Each Wrong Option is Incorrect**
**Option A:** Nail fold capillaroscopy is a technique used to examine the capillaries in the fingernails, but it is not the best diagnostic tool for Wilson's disease.

**Option C:** Biopsy of the pigmented area may not be necessary, as the diagnosis can often be made with a slit lamp examination. Additionally, a biopsy may not provide any additional information that would change the management of the patient.

**Option D:** Ankle-brachial pressure index is a test used to diagnose peripheral artery disease, which is not directly related to the symptoms and signs presented in this case.

**Clinical Pearl / High-Yield Fact**
Kayser-Fleischer rings are a classic sign of Wilson's disease, and their presence can confirm the diagnosis in a patient with neurological symptoms and a history of jaundice.

**✓ Correct Answer: B. Slit lamp examination**