Final answer:
A style of management where the manager is actively involved and encourages employee participation is known as hands-on or Theory Y management style.
Step-by-step explanation:
The style of management where the manager actively participates in the ongoing work at a facility and engages with employees is often referred to as a hands-on, participative, or Theory Y management style. According to Douglas McGregor's Theory Y, this approach assumes that employees are inherently motivated and can work productively on their own. Managers who employ this style typically believe in the collaborative nature of work and therefore encourage teamwork, solicit feedback, and allow employees to have a say in the decision-making process. This is in contrast to Theory X, which posits that employees are generally unmotivated and need constant supervision and control. The hands-on management style is known to foster a more engaged and collaborative work environment, whereby employees can contribute significantly to the success of the organization.