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Arizona is a state that shares a border with Mexico, making it the correct answer. The state has a significant geographical location along the southern edge of the United States, directly adjacent to the Mexican states of Sonora and Baja California. Arizona's border with Mexico is notable for its diverse culture, trade relations, and historical significance.

In contrast, Oregon, Idaho, and Washington are located in the Pacific Northwest region of the United States and do not share any boundaries with Mexico. These states are situated far to the north of the U.S.-Mexico border, emphasizing why they cannot be considered as neighboring states. Understanding the geographic locations of these states in relation to Mexico is crucial for recognizing which states directly border the country.