Final answer:
According to Ryan and Deci's self-determination theory, the need to be able to master the challenging task of one's life is the need for competence.
Step-by-step explanation:
Ryan and Deci's self-determination theory states that the need to master challenging tasks is a fundamental need known as competence. This need refers to the desire to feel capable and effective at achieving goals and succeeding in one's endeavors. According to the theory, when individuals feel competent, they are more motivated and engaged in their lives.