Uh oh, here we go! Before the Fediverse’s favourite mathematical charlatan comes to play, let’s lay out a few facts:

• This is an unusual way of writing down this expression: you would not normally mix in-line division (written with ÷) and multiplication written without a symbol. It’s written this way on social media to for engagement bait.
• Because of this, a perfectly valid reply is to ask “can you put in some brackets to make it clear” :)
• A strict, standard reading of the order-of-operations as abbreviated by PEMDAS, BODMAS, etc, is to perform multiplication and division in the order that they occur. This would mean the evaluation goes like this:
  1. 6÷2(1+2)
  2. Perform addition inside the brackets: 6÷2(3)
  3. Perform the first multiplication or division: 3(3)
  4. Perform the remaining multiplication: 9
• Occasionally, PEMDAS is interpreted as indicating that multiplication must be done first because the M occurs before the D. This is not usually how it is taught, but rarely it happens. This would give you 1 but, to be clear, in most places this is wrong. I myself was taught BODMAS and, in fact, do division first in all circumstances.
• Much more commonly, though, the actual practical order in which mathematicians, teachers and students all evaluate expressions is a little different, in that it evaluates symbol-less multiplication (also known as “juxtaposition” which just means “writing two things next to each other” or, in discussions about this topic in particular, “implicit multiplication”) before anything else. This is done because writing two things next to each other creates a tightly-bound visual unit.

It’s rare for this last point to be mentioned explicitly as a violation of the order-of-operations. It usually only becomes relevant well after those conventions are spelled out (which is typically done in late primary school or early high school) after children start learning algebra and how to write algebraic expressions: using letters to represent unknown quantities, omitting the × symbol. Exam boards and textbooks are usually quite careful to avoid writing problems in which this unstated rule actually matters.

It’s important to realise that the order in which we evaluate a mathematical expression is a matter of convention. After establishing how to add, multiply, subtract or divide two numbers, it is a separate question which operations should happen first when more than one is written together. This is why we need to teach students the order of operations - they can’t just work it out themselves. Having said that, it certainly makes a lot more sense to do multiplication before addition, and exponentiation before multiplication, because each of these operations is (typically: you can define them in different ways if you’re a masochist) defined in terms of the previous one. This means that if you have an expression involving all three, and you first turn all the exponentiation into multiplications, you are left with a simpler expression that means the same thing. This only happens if evaluating exponentiation is the first thing you’re supposed to do. However, it would be a mistake to think this means that there is any mathematical necessity about this: what a sequence of squiggles on paper means is entirely up to the people reading and writing the squiggles; as long as they agree, the person reading the squiggles will get the same answer as intended by the person writing them. There’s a good, lengthy write-up here

This means that while what I was taught is “wrong” according to how it is usually taught (including today in the same country), this wrongness is better understood mathematically as “unusual” - something that needs to be worked out by communication and consensus rather than by dictating one right and another wrong.

You do get some people with very strong opinions about this, which is not always correlated with their actual knowledge. If the aforementioned charlatan turns up, I’ll explain…