This clinical trial studies whether Acceptance and Commitment Therapy can be used to help improve cancer distress for patients with hepatobiliary or breast cancers for which no treatment is currently available (incurable). Patients with hepatobiliary cancer (HBC) and breast cancer often experience high levels of distress and reductions in quality of life. Acceptance and Commitment Therapy for incurable cancers (ACT-C) is a behavioral intervention tailored to patients with incurable HBC and breast cancer. It helps patients cope with difficult thoughts and emotions while staying connected to what matters most in life, which may be an effective way to improve cancer distress.