Lymphocytes are the cells that produce antibodies. Antibodies, also known as immunoglobulins, are proteins that are produced by the immune system in response to the presence of foreign substances, such as bacteria or viruses. These foreign substances are called antigens.

Option 1: Eosinophils are a type of white blood cell that are involved in allergic reactions and fighting off parasitic infections. They do not produce antibodies.

Option 2: Monocytes are a type of white blood cell that play a role in the immune response by engulfing and digesting foreign particles. They do not produce antibodies.

Option 3: Basophils are a type of white blood cell that release chemicals such as histamine during allergic reactions. They do not produce antibodies.

Option 4: Lymphocytes, specifically B lymphocytes, are responsible for producing antibodies. These cells are part of the adaptive immune response and are able to recognize specific antigens. Upon encountering an antigen, B lymphocytes produce and release antibodies that can bind to and neutralize the foreign substance. This helps in the elimination of the antigen from the body. Therefore, option 4 is the correct answer.

In conclusion, lymphocytes, specifically B lymphocytes, are the cells that produce antibodies.