Which option best describes a facility eligible for a dental hygienist to work in?

The best choice is one that highlights a facility where dental hygienists can legally practice within their scope under Washington State law. State-operated hospitals are eligible facilities because they often provide comprehensive health services, including dental care, and are authorized to employ dental hygienists to deliver essential services to patients. These hospitals may serve populations that require specialized care or those without access to private dental clinics, thereby aligning with the hygienist's role in promoting oral health.

On the other hand, private family clinics and individual practitioner offices are also valid environments for dental hygienists but may not capture the essence of facility eligibility as explicitly as state-operated hospitals. Local schools, while they can provide health education, typically do not serve as primary facilities for the practice of dental hygiene in terms of clinical care delivery.