Final answer:
The building under Roosevelt's right arm in the Big Stick Diplomacy cartoon likely represents the White House, symbolizing the authority of the U.S. presidency.
Step-by-step explanation:
The building shown under Roosevelt's right arm in the Big Stick Diplomacy political cartoon is likely indicative of the executive branch which the president heads, thus it could be the White House. The presence of this building would symbolize the authority of the U.S. presidency, aligning with the theme of the cartoon that portrays Roosevelt's assertive foreign policy approach, commonly referred to as 'Big Stick' diplomacy.