Final answer:
The international competition that Mexico made history with by hosting twice is the FIFA World Cup, this occurred in 1970 and 1986.
Step-by-step explanation:
In 1986, Mexico made history in the world of sports by becoming the first country to host a particular international competition twice. The correct answer is the FIFA World Cup. This marked the second time Mexico was given the honor of hosting this prestigious sports event, the first time being in 1970. The world's attention turned to Mexico as they successfully led the event despite the complex logistical challenges.
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