Final answer:
U.S. troops rescued the island of Grenada (A) from a Cuban-backed invasion in 1983, in an effort to remove a Communist government that came to power following a coup.
Step-by-step explanation:
The island that U.S. troops rescued from a Cuban invasion in 1983 was A) Grenada. The invasion, named Operation Urgent Fury, was undertaken by 7,000 US soldiers who overwhelmed and seized control of Grenada. This invasion occurred in response to a prior coup by Marxist rebels who had taken over the Grenadian government. These rebels were building a government aligned with Cuba and the Soviet Union, which was a concern for the United States during the Cold War era.
Two days following the bombing in Beirut, President Reagan and Secretary of State George P. Shultz authorized the invasion to oust a Communist military junta, that had overthrown a moderate regime. Although Communist Cuba had troops stationed on the island willing to defend the new regime, the United States successfully took command of the situation. The Cuban forces surrendered after just two days of conflict.