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.
References:
Bolognia, Jean., Jorizzo, Joseph L.Schaffer, Julie V. (Eds.) (2012) Dermatology /[Philadelphia] : Elsevier Saunders