This question is a cross post from chemistry. I'm not very convinced with the answer there. So, I'm posting it here.
I'm tutoring few students for Chemistry. During the course, I many times use the phrase "Out of these possibilities this one is stable. So it is formed". I get questions like, "How do the molecules know?"
Honestly I don't know. How do they proceed to form "Most Stable" compound?
Best Answer
Molecules don't know. Consider the following reaction as a template for some reaction that is favored to go in the direction indicated. \begin{align*} A-B +C \rightarrow A-C +B \end{align*} In a large collection of such molecules you can always find some $AB$ going to $AC$ and some going backwards. It is just that significantly more $AB$ are going to $AC$ so you when you look into your beaker (system/experiment) you see that you are forming $AC$.
Next question is why or when is $AC$ preferred? The process of the reaction is such that $AB$ is flying around doing its thing when $C$ smacks into with enough energy to form a transient state $B-A-C$. Now from this state it can forward $AC+B$ or go back to $AB+C$. This is the highest energy state and all the energy is jostling between these two "bonds" (interaction might be a better word). This state is called the transition state. For any particular set of molecules in your beaker (a large number ~Avogadro number) the path forward or backward has to go through this transition state.
Think of what it takes to get to the transition for any set of molecules. In going from $AB$ to $BAC$ it requires the $C$ to come in with kinetic energy that is the energy difference between the energy of $BAC$ and $AB$. Similarly to go from $AC$ tp $BAC$ it requires a $B$ to come in with kinetic energy that is the difference in the energy of $AC$ and $BAC$. It is now intuitive that if $AC$ has significantly lower energy than $AB$ it is less likely to find a higher kinetic energy $B$ than $AB$ finding a relatively less energetic $C$. This is why if $AC$ is the significantly lower energy product, i.e., the reaction above is exothermic the forward direction is preferred.
Caution: I have been a little sloppy in my explanation. Because there are many many particles in the system, many other reactions are possible, e.g., $AC$ splitting itself apart into $A$ and $C$, $C$ not hitting $AB$ from the $A$ side and forming $A-B-C$ instead of $B-A-C$ in which case it cannot form $AC$ it can only form $A+BC$ etc. All this is part of what defines the chemical kinetics of the system. Furthermore the fact that there are many instances of these reactions happening simultaneously, one can study this system using statistical means. This is what is done when one says "thermodynamically" the free energy $\Delta G$ is minimized in the reaction. I saw that people have given you that explanation in Chemistry so I will not reproduce it here.
Summary: A stable product is the one energetically favored or more precisely "free" energetically favored (lowest free energy). But molecules are going either way they don' know. More of them going the right way succeed! The ones that went wrong way eventually bump into guys that are going the right way are are forced to make a U turn.