How did kublai khan kill his brother?

Kublai Khan did not actually kill his brother, Ariq Böke; rather, their conflict arose during a civil war for control of the Mongol Empire after Genghis Khan's death. This rivalry led to a series of battles between their respective factions. Ultimately, after Ariq Böke's defeat, he was captured, and while Kublai offered him a position of power, Ariq Böke chose to commit suicide instead of submitting to Kublai's rule.