October 6th is not a national day holiday in the United States. However, there are several holidays and observances celebrated on this day, including:

• National Coaches Day: This day is dedicated to recognizing the important role coaches play in shaping the lives of young people.

• National Orange Wine Day: This day celebrates the ancient and underrated drink, orange wine.

• National Body Language Day: This day encourages people to try and understand each other better through nonverbal communication.

• National Transfer Money to Your Daughter Day: This day is dedicated to daughters receiving extra pocket money from their parents.

• National Mad Hatter Day: This day is a celebration of creativity, eccentricity, and imagination.

• Kids Music Day: This day encourages parents to make music with their children.

• National Badger Day: This day is dedicated to showing love and appreciation for the iconic animal, the badger.

• Manufacturing Day: This day celebrates American exceptionalism in manufacturing.

• World College Radio Day: This day is celebrated on the first Friday in October and is dedicated to college radio stations.

• National Diversity Day: This day is celebrated on the first Friday in October and is dedicated to promoting diversity and inclusion.

In addition to these holidays, there are several other observances and events that fall on October 6th, such as National Noodle Day, National Critical Illness Awareness Month, and National Liver Awareness Month.