**Core Concept**
The case description is suggestive of tinea capitis, a fungal infection of the scalp, characterized by boggy swelling, discharging sinuses, and easily pluckable hair. This condition is a common cause of scalp lesions in children.

**Why the Correct Answer is Right**
Diagnosis of tinea capitis involves demonstrating the presence of fungal elements in the scalp. This can be achieved through a potassium hydroxide (KOH) preparation, where a scalp sample is treated with KOH to dissolve keratin and reveal fungal hyphae. The KOH preparation is then examined under a microscope to confirm the presence of fungal elements.

**Why Each Wrong Option is Incorrect**
**Option A:** A biopsy would be more invasive and is not typically used for initial diagnosis of tinea capitis.
**Option B:** A culture may be used to identify the causative organism, but a KOH preparation is a more rapid and cost-effective method for initial diagnosis.
**Option C:** A Gram stain is not typically used for diagnosing fungal infections like tinea capitis.

**Clinical Pearl / High-Yield Fact**
Tinea capitis is a common cause of scalp lesions in children, and a KOH preparation is a quick and effective method for diagnosing this condition.

**Correct Answer: D. KOH preparation**