Option 1: Granulocyte - Granulocytes are a type of white blood cell that are involved in immune responses, but they are not responsible for the production of antibodies. Granulocytes mainly destroy invading pathogens by engulfing them or releasing toxic substances.

Option 2: Lymphocyte - Lymphocytes are the cells responsible for the production of antibodies. There are two main types of lymphocytes: B cells and T cells. B cells are the specific lymphocytes that produce antibodies. When a B cell encounters a foreign substance, such as a vaccine, it recognizes it and begins to produce antibodies that specifically target that substance. These antibodies can then bind to the pathogens and neutralize them, or mark them for destruction by other immune cells.

Option 3: Erythrocyte (Red Blood Cell) - Erythrocytes are not involved in the production of antibodies. Their main function is to transport oxygen to tissues and remove carbon dioxide from the body.

Option 4: Platelet - Platelets are involved in blood clotting, but they are not responsible for the production of antibodies.

Therefore, the correct answer is option 2 - lymphocyte.