How do I wire a/c if furnace wiring compartment has no y terminal?
This is easy

If your furnace board does not have a Y terminal, then you simply need to connect the Y wire from your thermostat directly to the Y wire to the outdoor unit (compressor) with a wirenut.  This way, the thermostat sends 24VAC to the compressor contactor to turn the A/C on during a call for cooling, as well as sending a 24VAC signal to the furnace fan relay to run the fan.