HC (Hydrocarbon) is raw fuel otherwise known as gasoline. The common reason vehicles fail the smog check for high HC is due to problems with the ignition system (spark), however your Ford Mustang's fuel delivery system has a lot to do with HC as well. The amount of HC left over after the combustion process is based on the amount of fuel having actually entered the combustion chambers. A "rich" or "lean" fuel mixture would contribute to high HC. Air/Fuel ratio must be at an optimum 14.7:1 in order to fuel to burn efficiently.
We recommend first inspecting your Ford Mustang's ignition system first. Check the spark plugs, spark plug wires, distributor, and ignition timing. If everything looks ok, move on to the inspection of the fuel delivery system, ie oxygen sensor (s), engine coolant temperature sensor, mass air flow sensor. Inspecting these components will require some auto emissions know-how and proper inspection tools.
The link below will give you a full list of problems which could cause high HC smog check failures.
What Causes High HC?