Final answer:
The Treaty of Kanagawa granted the United States trading rights at two Japanese ports, Shimoda and Hakodate. It was signed in 1854 and negotiated by U.S. Commodore Matthew Perry.
Step-by-step explanation:
The treaty that granted the United States trading rights at two Japanese ports is the Treaty of Kanagawa. This treaty was negotiated by U.S. Commodore Matthew Perry and was signed in 1854. It opened the ports of Shimoda and Hakodate to American trade and established a U.S. consulate in Japan. The treaty also ensured humane treatment and the return of shipwrecked American sailors.