Thank you for taking an interest in choosing a Nest thermostat for your home. I'd be happy to take a look into this for you.
Based on the wiring setup shown in the attached pictures, your thermostat has no label. To ensure your systems' compatibility with the Nest thermostats, do you mind me asking the make and model of your HVAC system and what type it is? Also, could you please send us a picture of your system's control panel showing how the wires are labeled?
Have a look at this article and let us know if you need more help.
Thanks for sharing the detail. It appears that you have a combi-type system with heat and cool.
To get a better result, do you have a picture of your system's wiring configuration? You can examine them in the control panel to see how we can label them.
I'll look forward to your response.