The average person doesn't understand PEMDAS (or BIDMAS as I was taught it), because it's a stupid arbitrary convention and cannot be applied consistently. It only exists because infix notation is inherently ambiguous, and it gets worse the more operators you add. The better rule would be simply: use brackets to denote the order of operations in all cases.

The right response to

    6 / 2(1 + 2)

is not "use PEMDAS", it's "syntax error".