The correct answer is B. Mastocytosis.
The patient presents with likely systemic mastocytosis, but definitively with diffuse cutaneous mastocytosis based on the appearance of the skin lesions and the c-KIT positive staining pattern.
T cell and B cell lymphoma are not correct as the staining pattern and infiltrate would appear differently in each of those conditions. Congenital syphilis would not stain positive for c-KIT, though syphilis should be on the differential diagnosis clinically. Neuroendocrine IHC markers, such as CD56, chromogranin A, and synaptophysin would be present in the case of neuroblastoma.
Valent P, Akin C, Hartmann K, et al. Advances in the Classification and Treatment of Mastocytosis: Current Status and Outlook toward the Future. Cancer Res. 2017;77(6):1261–1270. doi:10.1158/0008-5472.CAN-16-2234