In each of the question given below, a statement has been given with a blank. Some words or phrases have been given in the options following the statement. Choose the most appropriate word or phrase that could fit in the statement to make it contextually meaningful and grammatically correct.

The English won several fortified battles, but in the end, the Americans were able to win the _____________.

The correct option is war.

Step 1: Analyze the context of the sentence
The sentence reads: "The English won several fortified battles, but in the end, the Americans were able to win the _____________."
The conjunction "but" sets up a contrast between winning individual "battles" and achieving ultimate victory overall. In military history and language usage, battles are specific, localized standard engagements, whereas a war is the broader conflict comprising many battles. Winning battles does not automatically guarantee winning the overall war.

Step 2: Evaluate the given options
• amity: Means peaceful relations or friendship, which does not fit the context of winning a conflict.
• truce: Refers to a temporary cessation of hostilities, which is agreed upon rather than "won".
• cease-fire: Similar to a truce, an agreement to stop fighting temporarily.
• war: Refers to the overarching military conflict composed of multiple battles, making it the perfect word to contrast with "battles".

Conclusion:
The word "war" fits both contextually and grammatically to complete the sentence meaningfully: "The English won several fortified battles, but in the end, the Americans were able to win the war."