Final answer:
The behavior described, involving repetitive organizing and checking of a closet, is known as a compulsion, typically associated with Obsessive-Compulsive Disorder (OCD).
Step-by-step explanation:
The term commonly used to describe the behavior of spending several hours a day organizing and reorganizing a closet, and repeatedly checking to see if clothing is arranged in the proper order, is compulsion.
Compulsions are repetitive behaviors that a person feels driven to perform in response to an obsession, or according to rules that must be applied rigidly. This term is often associated with Obsessive-Compulsive Disorder (OCD). While obsessions are persistent, unwanted thoughts, urges, or images that are intrusive and cause distress or anxiety, compulsions are the repeated actions taken to reduce the anxiety associated with these obsessions.