Question

Who are the men who are shown in the fun for the boys cartoon

Answer 1

The men shown in the "Fun for the boys" political cartoon are:
William McKinley, Theodore Roosevelt, and William Howard Taft.

Hope this helps. 

Answer 2

The "Fun for the Boys" cartoon by William Bengough published on August 23rd, 1900 shows William H. Taft, Theodore Roosevelt, and William McKinley. In this anti-imperialism cartoon, these men are revising the declaration of independence and editing it. There's a ghost watching them as they do so and that is George Washington, who looks as very deep in thought.

W. Bengough is clearly against the US for acquiring the Philippines after Spain lost a war to the United States. The Philippines were outraged as they were seeking independence.