Why does the a/c compressor come on a 2004 explorer when you turn controls to heat for air to come from dash vents air comes out cold and a/c is running when I want heat

SOURCE: 2004 ford explorer heating

Check the heater control valve, when u switch to heating mode, this valve is supposed to open, allowing hot engine coolant into the heater core under the dash, it is not opening the valve, the clicking is the sound from it attempting to open the valve.

SOURCE: 2003 Ford Explorer is knocking and blowing cold air when I turn the knob to the heat

The blend door (mode door ) is a very common issue there is even an associated TSB t(technical service bulletin) it has to do with the blend door becoming warped and binding the accuator. In an opened or semi-closed position

SOURCE: 2004 F150 Heater Vent Selector Problem

The "blend door" or "mode selector door" is stuck. Common problem with Fords. Most auto repair places can fix it. I had mine done at Firestone.

SOURCE: Vent control

You have a vacuum leak.Defrost is the default postion(no vacuum).
See if you can locate the small black vacuum line that goes inside the vehicle on the passenger side near the heater core. The trace it back,should see it going to a canister then to the intake manifold.Make sure it is not disconnected or broken somewhere.

SOURCE: PROBLEM WHEN SELECTING THE DIRECTION FOR THE AIR

Sounds like you have a supply vacuum problem. When you lose supply vacuum to the control head it defaults to defrost.