Final answer:
The federally funded health care financing mechanisms mentioned in the question are Medicare and Medicaid, with Medicare serving primarily those over 65 and disabled individuals, and Medicaid being available to those with very low incomes.
Step-by-step explanation:
The various types of health care coverage include both privately funded and federally funded options. The federally funded health care financing mechanisms include Medicare and Medicaid. Medicare offers health services primarily to people over 65 years old as well as to others who meet disability standards. Medicaid provides services to people with very low income who meet specific eligibility requirements. On the other hand, Preferred Provider Organization (PPO) and Exclusive Provider Organization (EPO) are types of managed care organizations that typically involve private funding, not federal. Long-term care insurance is also usually privately funded. Thus, the federally funded health care programs mentioned in the question are Medicare and Medicaid.