Which part of Operation Downfall was planned to invade Japan’s island of Kyūshū?

Operation Olympic was the part of Operation Downfall planned to invade Kyūshū.

Olympic was intended to begin on November 1, 1945, with Allied landings on the southern portion of Kyūshū, Japan’s southernmost main island. Capturing that area would have provided airfields and staging bases for the later phase of the invasion plan.

The second phase, Operation Coronet, was planned for the Kantō Plain near Tokyo on Honshū in spring 1946. Together, Olympic and Coronet made up Operation Downfall, the proposed invasion of Japan’s home islands.

Olympic was never launched. Japan’s surrender followed the atomic bombings of Hiroshima and Nagasaki, the Soviet entry into the war against Japan, and the Soviet invasion of Manchuria. Because Olympic and Downfall were canceled, estimates of likely casualties remain hypothetical and vary widely among historians.