Dose any one knows how a pneumatic thermostat work?
And the compressor attach to a air handel unit

Pneumatic and hydrolic thermostats and there associated pumps and selonoids/relays are a speciality item usually only encountered in commercial HVAC settings. I am very well versed in these controls but I do not feel like writing a book to cover exactly how they work. You might do a Google and search for a manufactures web site which will have a detailed diagram and other information for you.

Pneumatic thermostats function in a number of different ways, one way is by sending air pressure to or relieving pressure from a pneumatic actuator or water valve to allow hot or cold water through a coil in the air stream or open or close a damper in the duct to allow or disallow hot or cold air to pass through duct, this is only a few ways they may work and also become very sophisticated.