Your final answer is correct, but you have a 2 in there where you shouldn't have. You have 2x = 2460/2 when you should just have x = 2460/2. Do you see it? If you actually solved the equation that you wrote down in the first line correctly, your answer would be 615.

Your solution should look like this:

Let her airfare be x, then twice as much as her airfare would be 2x. She spent $60 dollars less than that. So she spent 2x - 60 dollars. She spent $2400 in all, so:

2x - 60 = 2400

=> 2x = 2460

=> x = 2460/2

=> x = 1230

So her airfare was $1230