The correct answer is B. Hepatitis C.
This is an example of necrolytic acral erythema, which is associated with chronic hepatitis C infection.
Hepatitis B is associated with classic PAN, among other conditions. HIV is associated with many dermatoses. HTLV-1 is associated with mycosis fungoides. TB can be associated with Erythema Induratum and tuberculid reactions. None of the above conditions is classically associated with necrolytic acral erythema.
Bolognia, Jean., Jorizzo, Joseph L.Schaffer, Julie V. (Eds.) (2012) Dermatology /[Philadelphia] : Elsevier Saunders