I suspect that Prof. George Bergman (Univ. of California, Berkeley) might disagree with you.
Please see: math . berkeley . edu / ~gbergman / misc / numbers / ord_ops . html
P.S., I completed my first year Calculus by the time I completed high school. I won’t bore you by listing the mathematics classes I completed in college and graduate school.
The problem is that the notation 2(3) (or more generally, the notation ‘ab’ in algebraic terms) is not addressed in either BODMAS or PEMDAS. This leads to ambiguity in how one is to interpret the equation. Because of that ambiguity, 10 and 58 should be accepted as the correct answer.
The question is whether you interpret 6^2÷2(3) + 4 as (((6^2)÷2)•3) + 4 or as ((6^2)÷(2•3)) + 4. If you interpret as the first you get 58 and with the second you get 10. ‘2(3)’ is an acceptable (in some circles) notation for ‘2•3’. If we use that as a semantic substitution in the original equation you have 6^2÷2•3 + 4. Since multiplication and division are of equal precedence, we proceed in a left to right evaluation. That would seem to indicate that the first interpretation is correct and the answer is 58. However, some interpret juxtaposition (i.e., 2(3) ) as a precedent between exponentiation and multiplication-division.
The ambiguity in notation might be better illustrated by the algebraic formula ‘a / bc’. If one uses a strictly left to right interpretation, it would be evaluated as (a÷b)•c, whereas if you interpret juxtaposition as a higher precedence than multiplication-division, it would be evaluated as a÷(b•c).
The underlying problem is that there is not an accepted precedence for either the slant (‘/’) or the juxtaposition notations. So either 58 or 10 can be accepted as the correct answer.
Maybe you should have said: show your work and your assumptions.
I had to put a blank space before and after the plus sign to get it to work.