During the spanish-american war, the united states pledged to support the people of

Correct  Cuba

The Spanish-American War was fought in 1898, after the USS Maine exploded in the Havana harbor of Cuba.  The USA blamed Spain for the explosion, though that has not been verified.  The main issue of the war was the independence of Cuba from Spanish dominance.

In early July, 1898, the US Navy won the last major naval confrontation of the war, at the Battle of Santiago.  The siege of the city of Santiago itself followed, from July 3-17.  At the end of the siege, both the US and Spanish government agreed to  terms of "capitulation" (avoiding the term "surrender," though that's what it was).  Spanish troops exited Santiago on July 17.

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