Step 1: Recognise the lesion.
A black/dark pigmented lesion on an acral site such as the heel or sole is highly suspicious of acral lentiginous melanoma, the commonest melanoma subtype in dark-skinned and Asian populations. Any new, irregular, pigmented acral lesion must be assumed malignant until proven otherwise.
Step 2: Choose the investigation.
The definitive diagnosis of melanoma is histopathology. An excisional biopsy (ideally full-thickness, removing the entire lesion with a narrow margin) is preferred because it allows accurate measurement of Breslow thickness, which determines prognosis and further management.
Step 3: Why the other options are wrong.
KOH mount detects fungal elements (e.g., tinea nigra), but a frankly suspicious black acral lesion in this setting demands tissue diagnosis, not just a fungal screen. Gram stain identifies bacteria and is irrelevant to a pigmented neoplastic lesion. Tzanck smear detects acantholytic/multinucleate giant cells in vesiculobullous and herpetic lesions, not pigmented tumours.
Key fact: A suspicious pigmented acral lesion (possible acral lentiginous melanoma) requires biopsy with histopathology and Breslow thickness - biopsy is the investigation of choice.