The 6th house is the house of service/work, our daily activities, care and concerns, illnesses and pets. Accordingly, the Moon in the 6th house shows a person who is constantly in a state of care, domestic bustle and chores. This manifests both at home and in the work environment.
However, the opposite polarity can also be expressed - laziness, passivity, and the need to offload work onto others.
But more often, it's a need to be needed. The Moon in the 6th house is oriented towards interaction with other people through empathy and helping others. Therefore, such people often choose professions related to care and assistance - nurses, nannies, educators, social workers, possibly chefs in the food industry. They usually don't strive for managerial positions, but the work environment should have a cozy, emotionally warm atmosphere.
The 6th house also deals with the theme of animals. And a person with the Moon in the 6th house may constantly be caring for, helping and feeding sick cats, dogs, and stray animals. They often have one of these "lesser brethren" at home as well.