2002 Ford Taurus heater core

Disconnect both hoses that go to the heater core from either end, (the end at the heater core or the end at the water pump, manifold, radiator, etc.) using a garden hose, preferably with a hose repair end attached to plug into the hose or a short piece of hose cut off to connect to the heater core, run water in each direction through the heater core until water runs clear, then reverse direction of flow. Repeat as many times as necessary until flow is restored and water runs clean. Be sure to also flush the rest of the cooling system or debris from it will likely just clog up the heater core again.