2+(4x3) gives the right answer, with addition coming before multiplication
If we rewrote all of Maths so that addition came before multiplication, then no, 2+3x4 would no longer mean what it does now (because + and x would have to mean something different to what they do now in order for the order to be swapped). The order of operations rules come directly from the definitions. You canβt just say βweβll do addition firstβ without having defined what addition is now, nor multiplication. In a world where addition comes before multiplication, that means multiplication is no longer shorthand for addition (because thatβs the very thing which means we have to do multiplication before addition, so it canβt be true anymore if now weβre doing addition first).
Letβs take an imaginary scenario where we now use x for add, and + for multiply. That would indeed mean that + has to be done before x, but note that + now means multiply. That means your βaddition firstβ 2+(3x4) is what we currently mean by 2x(3+4) which is 14. Now take away the brackets (since I donβt use brackets when adding up the milk! Just 2+3x4). Your addition-first 2+3x4 is equivalent in our multiplication-first world to 2x3+4 which equals 10 - the wrong answer! So now youβve created a world where we have to add brackets to things just to get the right answer! Why would you even want to do that when it works the way it is? The whole point to having order of operations rules is to not have to add brackets!