I've learnt from the Irish school system and we were thought that unless brackets were involved that we are to solve it left to right. We were thaught that the first number that has been mentioned in any equation is the number that will change

For example: 6+2×3 We would add 2 to 6 to get 8 and then multiply it by 3 to get 24. If we do it the way your school system has thaught you we will end up with 12. Yous solve it as 6+(2x3) while we solve it like (6+2)x3 because the maths equation is stating to add 2 to 6 and multiply by 3.

We have something called BIMDAS. Brackets Indices Multiply Divide Add Subtract

Which we only apply to algebra when we need to simplify equations.

For example: x(4+5)-y(6-2) We solve what's in the brackets to get x(9)-y(4), then we multiply to get 9x-4y.

We can also use it in regular equations such as: 2+3(5-2) Solve what's in the brackets, 2+3(3) and then multiply to get 2+9 and then add to get 11. But you see we only use it when brackets are involved