Oh no, not again!
Threads about the order of mathematical operations tend to run to dozens of posts here on AB, with plenty of argument about what's 'right' or 'wrong'.
My own view (as a maths graduate who's taught the subject up to A-level) is that what's really 'wrong' is the expression given in your question. Mathematics is all about clarity and that expression fails to make it completely clear (in away that nobody here could possibly argue about or misunderstand) as to what the required order of operations is. I'd be reaching for my red pen if a student of mine had ever written it down like that! For clarity it needs some additional brackets.
However the reason that the answer is 9 is defined by 'BODMAS', which has been taught in schools for centuries. (Not by me though! I insisted on seeing some additional brackets to clarify things!!!). That's explained here:
https://www.skillsyouneed.com/num/bodmas.html
Looking at your expression
8 + 2 ÷ (4 - 2)
and applying BODMAS tells us that the first thing to deal with is what's inside the brackets, giving us
8 + 2 ÷ 2
Then, because division takes priority over addition, it's the division that has to be carried out next, giving us
8 + 1 = 9