T lymphocytes are responsible for:

T lymphocytes, also known as T cells, are a type of white blood cell that is an essential part of the immune system.
T cells are one of two primary types of lymphocytes — B cells being the second type — that determine the specificity of immune response to antigens (foreign substances) in the body.
T cells can be distinguished from other lymphocytes by the presence of a T-cell receptor (TCR) on their cell surface.
T cells originate in the bone marrow and mature in the thymus.
After migration to the thymus, the precursor cells mature into several distinct types of T cells.
One of these types is the CD8+ T cell, also known as cytotoxic T cell, which is responsible for cell-mediated immunity.
Cell-mediated immunity is the type of immunity that involves the direct killing of infected cells and cancer cells by cytotoxic T cells.
Choice A is wrong because humoral immunity is the type of immunity that involves the production of antibodies by B cells and plasma cells. 
Antibodies are proteins that bind to specific antigens and mark them for destruction by other immune cells.
Choice C is wrong because programming macrophages is not a function of T lymphocytes.
Macrophages are a type of phagocytic cell that can engulf and digest pathogens and cellular debris.
Macrophages can be activated by cytokines, which are chemical messengers secreted by helper T cells and other immune cells.
Choice D is wrong because producing antibodies is not a function of T lymphocytes.
As mentioned above, antibodies are produced by B cells and plasma cells, which are another type of lymphocyte.