ok reversing valve was connected directly from contactor and relay, ky teacher said it supposed to have 24 to 30 volts; ok i disconnected and put 27v and reversing valve did not turn on;
question it possible a reversing var work with 120 voltage?
if i put low voltage 27volt and i never heard nothing, and still not cold air?

The coil for the valve can be bad. The valve can be stuck also. Turn off unit remove coil and put 24 volts directly on the coil tahe a small screw diver and put it hole on coil. See fit it will create a maginet effect on the screw driver. If it does the coil is ok. Most coils are 24 volts but you can look on the wiring diagram on the door of the unit and see what voltage is feeding the coil.

the wiring diagram was 208v, the relay was bad , i had it fix , thanks to you. great
i am learning with you what i did not with my teacher.

The funny part is I teach this stuff sometimes at a local university in KY. But I bet I was not your teacher. NKU a few times a month and research the rest. I do not actually work there for $$$ since I teach Augratis (for free). I am to old to get paid for what I do (LOL) but I do enjoy helping some young and intelligent people get better at what they want to do.. LOL.