Final answer:
The federally funded health care financing mechanisms being referred to are Medicare and Medicaid, which provide coverage for the elderly, disabled, and low-income individuals respectively.
Step-by-step explanation:
Among the various types of home health care coverage, the federally funded health care financing mechanisms are Medicare and Medicaid. Medicare primarily offers health insurance to individuals over the age of sixty-five as well as to people with certain disabilities.
Medicaid is another federal program that provides health coverage for individuals and families with low income and resources. The other mechanisms mentioned, such as Preferred Provider Organizations (PPOs) and Exclusive Provider Organizations (EPOs), as well as long-term care insurance, are typically privately funded and not federally funded.