For this question, our goal is to determine how many antigens each molecule can bind. This will require some background knowledge, and it might be helpful to look at a figure or model for each of the proteins.
Each antibody can bind to 2 antigens, one on each of the two "arms." It can also bind to the immune system cell for a total of 3 attachment sites.
One Fc molecule
The Fc domain of an antibody is the crystallizable region that interacts with the cell surface. This region of the antibody only interacts with one antigen.
One molecule of IgG treated with BME
(2-mercaptoethanol) is a drug that weakens antibodies by interacting with the active sites. Therefore, this antibody can only bind to a maximum of one antigens, though likely it cannot bind to any.
One molecule of IgG with Cys Ser mutation.
Even though there is a mutation, Cys and Serum are both neutral polar amino acids. Therefore, there is little change in the active site and the antibody can still bind to its antigens, though perhaps not as strongly depending on the specific interaction.
One Fab molecule
The Fab domain is the fragment, antigen binding region. Each antibody contains 2 Fab domains, and each is able to bind one antigen.
One molecule of IgG treated with papain
Papain cleaves the antibody in the hinge domain, creating three separate molecules: tow Fab domains and one Fc domain. Each domain keeps its binding specificity, however, so we now have three molecules which each have one binding domain.