The wire on the R contact on your thermostat (should be a red wire) is +12 VDC coming in. You want to jumper that to the Y contact (yellow wire) to start the AC compressor. However, you also need to run the fan. The GW contact (green wire) is the high speed and the GL (gray wire) is the low speed. I'd go with the high speed. So you also need to jumper the R contact to the GW contact.
I've attached a wiring pic for installing a Honeywell Thermostat in place of a Coleman Mach thermostat. So look at the wiring on the left side, and jumper R to Y & GW.
(Note: Don't worry about the blue wire, which is ground. You don't need this, because all it does is supplies a ground path for the brains in the thermostat, which you will no longer be using. You'll see the Honeywell doesn't need it either, because the brains in the Honeywell are battery powered.)
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