How does vaccination produce immunity towards a particular disease?

The correct option is B It stimulates lymphocytes to produce antibodies.
The vaccines contains the antigens or the antibodies of the specific microbe which is responsible for causing disease or infection. The vaccines causes generation of an immune response and the information of the specific antibody is stored in the memory cells. This provides protection or resistance against the attack of the disease as the antibodies will be produced by the B-lymphocytes on the second encounter.

Thus, the correct answer is option B.