Schools only started teaching that rule relatively recently

Recently? The order of operations rules have been taught for more than a century (we can see them in Lennes' letter).

Afaik the order of operations doesn’t have distributive property in it

The Distributive Law applies to all bracketed terms that have a coefficient. It's literally the first step in solving brackets.

Just proves, never too late to learn :-)

2+2 first because P. That’s 4.

P is 2(2+2)=(2x2+2x2)=(4+4)=8

Then 8/2 because it’s left of 4(4).

If you do 8/2 when you still have brackets, then you just did division before brackets and disobeyed order of operations rules. You also broke the rule of Terms, since 2(4) is a single term.

Don’t take my word for it.

I see you didn't read my thread then. I have a section on calculators, which points out that WolframAlpha does it wrong. i.e. they also break the rule of Terms.

8/2(2+2) = 8/2(4)

Then you do your exponents

You haven't finished Brackets yet! The next step is...

8/(2x4)=8/8

This is straight from the textbook

Not any textbook I've seen. Screenshot? Here's some actual textbooks

an actual PEMDAS Solver

I looked and it's actually wrong. With the exception of MathGPT, I haven't found any e-calcs which do it correctly.

That two numbers applied to division don’t form a term?

Now you're getting it! Correct, they don't. They form an expression. Terms are separated by operators, and joined by grouping symbols. Expressions are made up of terms and operators (since, you know, operators separate terms). I told you way back in the beginning that 1÷2 is 2 terms, and ½ is 1 term. Getting back to the original question, 2(2+2) is 1 term and 2x(2+2) is 2 terms.

you find yourself an authority that you trust

Which time that I mentioned textbooks, historical Maths documents, and proofs did you miss?

university professor

University professors don't teach order of operations - high school teachers do. That's like saying "Ask the English teacher about Maths".

If you want to continue this

Why would I want to when you ignore Maths textbooks and proofs? See my first comment in this post that you've finally got the difference now. See ya.

‘this particular notation is the notation!’ to ‘of course other notations exist’

The notation for division in some countries is the obelus, in other countries it's a colon. Whatever country you're in, the notation for that country is the notation for division (be it an obelus or a colon).

Maths,” do you mean the notation on paper, or the underlying laws-of-reality stuff

Both! Whatever notation your country uses, all the rules for Maths and use of that Maths notation are defined.

It’s ambiguous

No, it's not.

It’s not distribution. It’s evaluating the parenthetical

And Distribution applies to brackets/parentheses where they have a coefficient. In other words, same same.

it’s 3 and -6, not 3 - 6

You didn't put a comma between 3 and -6, so no, it's not 3 and -6, it's 3-6. That's what you wrote, that's what it is.

a state trusts you with the education of children

Related - have you noticed how children never get this wrong? It's only adults who've forgotten the rules of Maths who get it wrong.

According to the textbook you’re now screenshotting at people, A(B) and (B)A are both correct - yes? They’re both valid? And spaces have no impact on an equation? And writing equations like -6 + 1 are fine, instead of (-6) + 1, since you don’t want needless parentheses?

Yes (though the latter is unconventional), yes (though the latter is unconventional), yes, yes (though unconventional - 1-6 is the conventional way to write that), yes, yes.

Show me a math textbook that says implicit multiplication

Show me a Maths textbook that says "implicit multiplication"! There's no such thing as implicit multiplication, just The Distributive Law and Terms.

The one you have shown does not say that.

So you're telling me you didn't see them do brackets first? 😂

Especially when said person keeps making incorrect statements about Maths and ignores completely what is taught in high school.

Regarding your second point I tried to address that in the “distributive property” section,

When I discovered this comment I went to read it, and yes, it's true you discussed the Distributive Property, however, what these people are talking about is The Distributive Law which isn't the same thing (though people often call it the wrong name), and makes the question completely unambiguous. You literally can't move on from the "B", Brackets, in the rules until there are no brackets left - the B is literally short for "solve Brackets" (every letter is "solve (something)"), and so anyone who does the division before solving the brackets has just violated the order of operations rules.