Most likely yes you can.
It looks like a Heat and AC system?
What kind of heat do you have? Hot air with ductwork or hot water boiler with radiators?
To check for sure you need to remove the screw near bottom of Tstat with the flat blade head. The swing the tstat up and remove from the base. Then you will see the wires connected to the base.
Take a pic of the base showing the wires.
Also note if you see any unused wires in the thermostat cable coming out of the wall.
Most likely you do not have a C common wire but if you have an unused wire you might be able to connect it to use as a C wire.
I'm just checking in to make sure that you've seen our response. Please let us know if you have any other questions or concerns as I will be locking this in 24 hours.
Awesome! We're glad to know that you've successfully installed your new Nest Thermostat. So, now that we can consider this finished, I'm going to lock this thread for 24 hours. If you have any other concerns or questions, please feel free to create a new thread.
Thanks for assisting, Edward.