This looks like a package unit - outdoor unit, all in one with the compressor, coils, and furnace/ air handler contained in one enclosure.
The yellow wire in this wire nut on that contacter should be the Y wire.
The blue wire on the other side of the contacter coil will be the common or C wire. Make sure the power is off when working inside this unit, The high voltage terminals are exposed and would be easy to accidentally brush your hand against.
The easiest way to hook up the C adapter would be to cut the blue wire inside the furnace and splice in another length of wire to it and run that wire to the outside of the unit where the other wire nuts are.
Whatever color that new wire is, it should be labeled C, and connected to the C wire on the C adapter. Then you would attach the yellow Y wire from the furnace to the Y wire on the C adapter, and the blue Y wire from the thermostat to the terminal strip on the C adapter. The Red wire coming from the furnace would be connected to the R wire on the C adapter, and the Red wire from the thermostat would be connected to the R terminal. The White wire coming from the furnace should be connected to the W wire on the C adapter, and the white wire from the thermostat should be connected to the W terminal on the C adapter. Lastly, the Green wire from the furnace should be connected to the G wire on the C adapter, and the green thermostat wire should be connected to the G on the terminal strip.
Then you would connect the green wire at the thermostat end of the wire to the C terminal on the wyze.
