Final answer:
The foreign policy that embarrassed the United States during the Kennedy administration was the Cuban Missile Crisis, when the Soviet Union placed nuclear missiles in Cuba.
Step-by-step explanation:
The foreign policy that embarrassed the United States during the Kennedy administration was the Cuban Missile Crisis. During this crisis in 1962, the Soviet Union placed nuclear missiles in Cuba, just a few hundred miles from Florida, which escalated the Cold War standoff with the United States. President Kennedy implemented a naval blockade of Cuba, forcing the Soviets to remove their missiles in exchange for the United States removing its missiles from Turkey.