Thanks for including such a good photo with your question. That makes things much easier.
The 4 wires you have available should work just fine for your new thermostat, but you won't have as much control over certain features (like air circulation). The wire colors on yours aren't hooked up according to the common standard, but as long as each wire is connected to the same terminal on both ends, you are just fine. This is what each wire is doing in your picture:
- Rh = 24V AC power - this provides power for the heating controls. (This wire is normally red - it is the red one in your picture)
- Rc = 24V AC power - this is commonly used to provide power for the cooling controls (if they are separate). If you only have one control system for both heating and coooling, it is common to only use Rh and provide a small jumper between the two terminals) (This wire is the blue one in your picture)
- Y = Call for Cooling - this provides the signal from the thermostat to run the cooling (This wire is normally yellow - it is the green one in your picture)
- W = Call for Heating - this provides the signal from the thermostat to run the heating (This wire is normally white - it is the yellow one or very faded white in your picture)
The unused G terminal on your picture is used to call for air circulation without heat or cooling (this is optional since circulation always runs when heating and cooling are running). You wouldn't have enough wire to make that work in your situation.
If you want a new thermostat that is battery powered, you'd be good to go with what you have. However, if you want a new smart thermostat, you'll need to provide it power from the furnace side. You can likely repurpose the blue wire, depending on what it doing at your furnace end. If you could provide a picture of that, that would be great.
UPDATE
Make sure you don't have two separate cables there - if the wire on that W terminal is really a faded white one rather than a yellow, then you have two separate cables - presumably one that goes to the furnace and one to a separate air conditioner. In that case, you might have an unused second red to work with.
Also - see if you can tug a bit on the cable or cables coming into the thermostat. Sometimes if there is some slack installers will just push it into the wall hole to get it out of the way. If you had enough slack, you could pull enough out to use that white wire.