Short answers, pulled from the story.
Operation Ke was the Japanese withdrawal from Guadalcanal, carried out between the 14th of January and the 7th of February 1943. It successfully evacuated 10,652 surviving Japanese troops from the island, concluding the six-month Guadalcanal Campaign. The operation was disguised as a reinforcement effort and was not recognized as an evacuation by Allied forces until it was already complete.
Operation Ke was directed by the Japanese Imperial General Headquarters, with Admiral Isoroku Yamamoto and General Hitoshi Imamura among the key commanders. The destroyer evacuation runs were led by Rear Admiral Shintaro Hashimoto, who commanded the Reinforcement Unit at the Shortland Islands.
A total of 10,652 Japanese troops were evacuated from Guadalcanal across three destroyer runs on the nights of the 1st, 4th, and the 7th of February 1943. Six hundred of those evacuated died from injuries or illness before receiving adequate medical care, and 3,000 more required lengthy hospitalization.
Japan withdrew because repeated attempts to recapture Henderson Field had all failed with heavy losses, and Japanese ground forces on the island had been reduced from 36,000 to roughly 11,000 through starvation, disease, and combat. The Imperial Japanese Navy was also suffering unsustainable losses trying to resupply and reinforce the garrison. Emperor Hirohito formally endorsed the decision to withdraw on the 31st of December 1942.
Japan used deceptive radio traffic around New Guinea and the Marshall Islands to suggest an impending offensive rather than a retreat. Japanese forces also changed their radio communication codes on the 1st of January 1943, making Allied interception harder. Allied intelligence correctly identified the operation by its code name Ke but misidentified it as a new offensive, not a withdrawal.
Japanese soldiers too sick or injured to move were ordered to kill themselves to uphold the honor of the Imperial Army. A small number of stragglers remained on the island after the evacuation; many were killed or captured by Allied patrols in the years that followed. The last known Japanese holdout on Guadalcanal surrendered in October 1947.