Maybe I'm wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.

"I saw her duck"

Until the author gives me clarity then that sentence has multiple meanings. With math, it doesn't click for people that the equation is incomplete. In an English sentence, ambiguity makes more sense and the common sense approach would be to clarify what the meaning is

So let's try out some different prioritization systems.

Left to right:

(((6 * 4) / 2) * 3) / 9
((24 / 2) * 3) / 9
(12 * 3) / 9
36 / 9 = 4

Right to left:

6 * (4 / (2 * (3 / 9)))  
6 * (4 / (2 * 0.333...))  
6 * (4 / 0.666...)  
6 * 6 = 36

Multiplication first:

(6 * 4) / (2 * 3) / 9  
24 / 6 / 9

Here the path divides again, we can do the left division or right division first.

Left first: 
(24 / 6) / 9  
4 / 9 = 0.444...

Right side first:  
24 / (6 / 9)  
24 / 0.666... = 36

And finally division first:

6 * (4 / 2) * (3 / 9)  
6 * 2 * 0.333...  
12 * 0.333.. = 4 

It's ambiguous which one of these is correct. Hence the best method we have for "correct" is left to right.

on that note, can we please have parentheses in language. i keep making ambiguous sentences

G U I N U S.

I know it's probably a typo, but I'm enjoying it.

on that note, can we please have parentheses in language. i keep making ambiguous sentences

So order of operations is hard?

The same priority operations can be done in any order without affecting the result, that's why they can be same priority and don't need an explicit order.

6 × 4 ÷ 2 × 3 ÷ 9 evaluates the same regardless of order. Can you provide a counter example?

100% with you. "Left to right" as far as I can tell only exists to make otherwise "unsolvable" problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.

The issue normally with these "trick" questions is the ambiguous nature of that division sign (not so much a problem here) or people not knowing to just go left to right when all operators are of the same priority. A common mistake is to think division is prioritised above multiplication, when it actually has the same priority. Someone should have included some parenthesis in PEDMAS aka. PE(DM)(AS)

Knowing basic arithmetic does not mean you know Math, and the fact you so hung up about this trivial aspect says a lot about you. Additionally, you express yourself like a boomer.

Except it does matter. I left some examples for another post with multiplication and division, I'll give you some addition and subtraction to see order matter with those operations as well.

Let's take:
1 + 2 - 3 + 4

Addition first:
(1 + 2) - (3 + 4)
3 - 7 = -4

Subtraction first:
1 + (2 - 3) + 4
1 + (-1) + 4 = 4

Right to left:
1 + (2 - (3 + 4))
1 + (2 - 7)
1 + (-5) = -4

Left to right:
((1 + 2) - 3) + 4
(3 - 3) + 4 = 4

Edit:
You can argue that, for example, the addition first could be (1 + 2) + (-3 + 4) in which case it does end up as 4, but in my opinion that's another ambiguous case.

My language teachers always told me it was bad form to use too much or even to nest parenthesis...

Then I found lisp...

I like the version where these problems are made purposefully ambiguous so people will fight over it and raise the level of interaction

I like the version where these problems are made purposefully ambiguous

None of them are ambiguous. They all have only 1 correct answer, just like this one only has 1 correct answer. They all test if people remember the order of operations rules. Those who got it wrong, don't.

No, it should simply be "Parenthesis, exponents, multiplication, addition."

A division is defined as a multiplication, and a substraction is defined as an addition.

I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when moving on from the simplified version you learn in elementary school.

That's because (strictly speaking) they aren't teaching math. They're teaching "tricks" to solve equations easier, which can lead to more confusion.

Like the PEMDAS thing that's being discussed here. There's no such thing as "order of operations" in math, but it's easier to teach by assuming that there is.

Edit:
To the people downvoting: I want to hear your opinions. Do you think I'm wrong? If so, why?

US teachers too lazy to teach kids actual maths did.

What’s lazy about learning PEMDAS? And what’s the non-lazy/superior way?

A division is defined as a multiplication

No it isn't. Multiplication is defined as repeated addition. Division isn't repeated subtraction. They just happen to have opposite effects if you treat the quotient as being the result of dividing.

Those two things are memorisation tasks. Maths is not about memorisation.

You are not supposed to remember that the area of a triangle is a * h / 2, you're supposed to understand why it's the case. You're supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it's stuck in: Start with the trivial case (right-angled triangle), then move on to more complicated cases. If you've understood that once, there is no reason to remember anything because you can derive the formula at a moment's notice.

All maths can be understood and derived like that. The names of the colours, their ordering, the names of the planets and how they're ordered, they're arbitrary, they have no rhyme or reason, they need to be memorised if you want to recall them. Maths doesn't, instead it dies when you apply memorisation.

Ein Anfänger (der) Gitarre Hat Elan. There, that's the Guitar strings in German. Why do I know that? Because my music theory knowledge sucks. I can't apply it, music is all vibes to me but I still need a way to match the strings to what the tuner is displaying. You should never learn music theory from me, just as you shouldn't learn maths from a teacher who can't prove a * h / 2, or thinks it's unimportant whether you can prove it.