To accurately answer your question about how the United States acquired the territory marked with the X, I would need to know which specific territory you are referring to. However, I can provide some historical context regarding the options you listed:
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By purchasing the land from Spain - This could refer to the acquisition of Florida, which the U.S. obtained through the Adams-Onís Treaty in 1819.
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By winning a war against Great Britain - This could refer to territories acquired after the War of 1812, but it’s not a specific acquisition that is typically highlighted in mentions of territory gains.
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By purchasing the land from France - This refers to the Louisiana Purchase in 1803, where the U.S. acquired a vast amount of territory from France.
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By winning a war against Mexico - This would refer to the territory gained after the Mexican-American War (1846-1848), including California and New Mexico.
If you can provide more context or specify which territory the "X" marks, I can give a more precise answer. Based on the historical options, if the territory is Louisiana, the answer would be "by purchasing the land from France." If it's California or parts of the Southwest, it would be "by winning a war against Mexico."