Final answer:
The antibody classes that can activate the nonspecific killing action of natural killer cells are IgG and IgM, making the correct answer D) both IgG and IgM.
Step-by-step explanation:
The antibody class able to destroy an antigen by activating the nonspecific killing action of natural killer (NK) cells through the mechanism known as antibody-dependent cell-mediated cytotoxicity (ADCC) is IgG. IgM can also activate the complement system leading to cell lysis, but its role in ADCC is not as well characterized as that of IgG. IgE is mainly involved in allergic responses and does not mediate ADCC in the same way that IgG does. Therefore, the correct answer is D) both IgG and IgM.