The statement that accurately evaluates the impact of the flow of goods, peoples, and ideas between the Old World and the New World during the sixteenth century is:
The flow of goods, peoples, and ideas caused long-reaching societal, cultural, biological, and agricultural changes on both sides of the Atlantic.
This statement recognizes the significant and transformative effects of the Columbian Exchange, which included the movement of crops, livestock, technology, and people, ultimately reshaping societies and ecosystems in both the Old and New Worlds.