The expression is 6÷2(1+2) and not 6÷2×(1+2)
Yes that × operation makes a huge difference. If the expression were written as the latter one, it would evaluate to 9. But since there is no × between them, it makes the 2 a coefficient of the bracket, and not simply a multiplier. And coefficients are evaluated first.
For example consider the expression "10a ÷ 5b" with a and b being unspecified constants. In such a case you will perform the 5×b operation before the division because it is a coefficient. This expression is (10×a)÷(5×b) and CANNOT be evaluated as (10×a÷5)×b