Here's the problem written step by step:

48/2(9+3)

48/2(12)

24(12)

288

Most people might argue differently, but here's why it equals out to 288. Once the Parentheses and Exponents have been solved, the rest of the equation is solved from Left to Right. Even though multiplication is before division in the order of operations, the Division of 48/2 is on the left side of the equation and therefore will be solved before the quotient of that equation is carried over to be multiplied by the sum of the parenthetical numbers. It's kind of hard to explain, but it's a very easy concept to grasp.