Final answer:
Mesoamerica is the agricultural hearth that grew maize, beans, and potatoes, and it independently began cultivating maize about six thousand years ago.
Step-by-step explanation:
The agricultural hearth that grew maize, beans, and potatoes is Mesoamerica. Maize agriculture initially began in Mesoamerica about six thousand years ago, and it is also the region that independently cultivated maize. Additionally, Mesoamerica is known for its cultivation of beans, which complement the nutritional value of maize and promoted the development of settled agricultural communities.