Final answer:
The leadership style that is caring and nurturing toward the employees' needs and well-being is Supportive leadership, according to Path-Goal theory.
Step-by-step explanation:
According to Path-Goal theory, the style of leadership that is demonstrated when the leader is caring and nurturing toward the employees' needs and well-being is Supportive leadership. Supportive leadership is characterized by showing concern for the followers' welfare and creating a friendly working environment. This contrasts with other styles such as Directive leadership, which involves giving explicit directions and guidance, Participative leadership, which encourages input and feedback from subordinates, and Achievement-oriented leadership, which sets challenging goals and expects high performance.