By knowing that a "dozen" represents a set of 12, and then either by adding them or by taking the shortcutmultiplying them! Multiplication is just fancy short-hand addition.
How do you know in this case? Did you get 2,688 eggs.
This particular problem has a real-world counterpart and can actually be proven as a natural fact.
You haven't proven that empirically.
You denied a "real-world" counterpart to polynomial equations I referenced earlier. On what basis? Algebra?
Do you multiply 12 times 224 or 224 times 12? Does it matter? How do you know? Empirically.
No, but I can buy them. I can also use 2,688 pebbles instead of eggs, and arrange them in groups of 12 each, then count the number of groups.
Luckily we invented shortcuts to physical counting, but if anyone doubts, the longer method is always available.
You haven't proven that empirically
I just have. But you are more than welcome to buy 244 dozen eggs and start counting. You don't have to take my word for it. You don't have to take my word for gravity either. A 20th flood seems like good starting point...to think about it on the way down. :)
You denied a "real-world" counterpart to polynomial equations I referenced earlier
Where is the real world application to those polynomial equations. Polynomials are used in optical design all the time, but their real-world counterpart can be carried only to two or three terms in a string of theoretically infinite number of terms. That is hardly a real-world counterpart, but an ideal real world appoximation.
An ideal is not a real-world counterpart but a fantasy. The perfect celestial spheres concept went out with Galileo. Of course, the Church was trying to tell him that the Moon was really unblemished and perfect, and that the devil (!) was distorting his view to make him think celestial bodies were imperfect. Why let reality get in the way of a perfectly concocted fantasy, right?
Do you multiply 12 times 224 or 224 times 12? Does it matter? How do you know? Empirically.
Sometimes I think sophism is a disease.