I think this might be clarified a bit by considering why we use the slant / for division.
Back when the earth was young and dinosaurs roamed the planet and I was an engineering student in college, we typed our reports on simple typewriters, not computer word processors. I doubt you young'uns remember those, so you'll just have to trust me a bit. Unless you had an IBM Selectric with interchangeable typeface balls, you had no way to type mathematical symbols. Plus and minus and multiply (+, -, x) were no problem, but for a divide symbol ÷ you had to type a colon : then back up and type a dash - through the middle of it.
That was a PITA and seldom looked good, so using a slash / was an alternative and was treated like a ÷ symbol. If we wanted a long expression in the denominator, we would use two lines, with the numerator
underlined (which was also a PITA) and the denominator typed below it. If we needed to fit it onto a single line, we'd use the / but with parentheses to show the denominator clearly.
Since the / was simply an alternative for ÷, the equation in question could be written as
8÷2x(2+2)
using conventional symbols.
We then evaluate it by solving the parenthetical expression first, then since only division and multiplication remain, we proceed from left to right.
8÷2x(2+2) = 8÷2x(4) = 4X4 = 16.
Multiplication and division are equivalent operations so there's no priority of one over another. We just proceed left to right.
This is exactly how all the computer languages I've used will evaluate it and it's how RPN will handle it. It's even how Excel evaluates it.
BUT, this is all rather ambiguous and can be confused easily. In any serious technical paper we would use brackets and parentheses to eliminate the possibility of error.