[spunkets]

"They ignore the distributive rule. If the problem was 48/2 x (9+3), 288 would be the correct solution, but that is not the problem."

That is the problem. You ignored commutativity. Factors commute, so 48/2 * (9+3) = 48(9+3)/2 = 288.

[SeaHawkFan]

Here is the problem as copied and pasted from the title of the thread:

48÷2(9+3) = ?

It is not 48 divided by two times (9+3)

There is a huge difference.