Final answer:
According to the Ann Arbor classification system, a patient with Hodgkin's disease with lymph node involvement on both sides of the diaphragm and involvement of the spleen has Stage III lymphoma.
Step-by-step explanation:
A patient with Hodgkin's disease who has lymph node involvement on both sides of the diaphragm and involvement of the spleen is classified as having Stage III lymphoma according to the Ann Arbor classification system. This system is used to stage Hodgkin's lymphoma based on the extent of lymph node involvement and the presence of other symptoms. In Stage III lymphoma, lymph nodes on both sides of the diaphragm are involved, which may include the spleen.