I was using bush trimmers and I accidentally cut the brown wire on my ac unit in half. I think it connects to the thermostat inside the house. How can I reconnect the colors and which colors goes to which?

If the wires were cut, strip back the outside insulation. You will see wires of different color. Strip about 1/2 " of insulation from each wire, solder or use a small wirenut, color to color, tape over the wirenuts to keep water out and you should be good to go.