Pasted below is a screenshot from this super interesting website: https://ciechanow.ski/bicycle/
Are the blue and green forces in the diagram below an action/reaction pair? If so, how does the process of equilibration described in the text make sense? If not, how would the drawing be changed to show the relevant reaction forces?
The blue and green forces are an action-reaction pair: the force that the box exerts on the wall is equal and opposite to the force that the wall exerts on the box.
At equilibrium, the force balance on the box is $$F_{red}=F_{green}$$ The blue force does not figure in the force balance on the box because, when we do a force balance on an object, we include only the forces exerted on that object by other bodies, not the force that the object exerts on them.
Are the blue and green forces in the diagram below an action/reaction pair?
Yes, the box pushes the wall and the wall pushes back the box.
If so, how does the process of equilibration described in the text make sense?
It considers a constant force and the elastic behaviour of the wall. I would say that the elastic behaviour of the box is more relevant, because by the picture it is a wooden box, more deformable than a concrete wall.
Are the blue and green forces in the diagram below an action/reaction pair?
Yes. The Blue and Green forces depict the pair described by Newton's Third law.
If so, how does the process of equilibration described in the text make sense?
Keep in mind that the process described in the text is occurring at the molecular level. Specifically, the website states that "the entire system very quickly finds its balance, and since the wall and box are very stiff, the final displacement isn’t perceptible."
The back and forth (equilibriation) motion that is being described is not actually perceptible. While this is not incorrect, it is also not incredibly useful to understand third law pairs in this way which seems to be the reason for your question in the first place.
For the sake of completeness, let's look at the other pairs as well:
The Red and Green forces are both acting on the same object. These cannot form a Newton's Third Law pair because the Third Law requires the forces to be acting on two different objects.
The Red and Blue forces do happen to be acting on different objects but are not acting in opposite directions (the other requirement of Newton's Third Law).
There is quite a lot of detail in the text that is wrong - but the art of physics is about ignoring irrelevant details. ;-)
You ask Are the blue and green forces in the diagram below an action/reaction pair? - the answer is yes. Every action has an equal and opposite reaction said Newton.
The next question is Are the red and green forces an action/reaction pair? - also yes if the box is stationary and stiff.
So your question boils down to Where does the red force originate?
