Final answer:
The code category used to report supportive care for a patient with a terminal metastatic carcinoma is Z51.
Step-by-step explanation:
The code category used to report supportive care for a patient with a widespread metastatic carcinoma that is terminal is Z51. This code category is used to report encounters for other specified aftercare, including supportive care, palliative care, and hospice care. In this case, the patient is admitted to a hospice unit for supportive care, so the appropriate code category to report this type of care is Z51.