Why would a Theory Y manager be more likely to use Maslow's Hierarchy of Needs to motivate employees?

He wouldn't try to motivate employees at all. This is because a Theory Y manager believes his employees are already self-motivated. He would focus on identifying and correcting any conditions that may destroy employee motivation.

An understanding of Maslow's work may help him identifying de-motivators. For example, dangerous working conditions trigger low-level needs for safety (on Maslow's scale). He would want to fix such a de-motivator so that employees can focus on satisfying higher levels needs that lead to positive behavior.