The correct answer is 3 inches.
To find this answer, we need to write and solve a quadratic equation.
Let's call the width of the frame X.
Then, the total width is 10 + 2x and the total length is 12 + 2x.
Having this information, we can write and solve the following equation.
(10 + 2x)(12 + 2x) = 288
4x^2 + 44x + 120 = 288
4x^2 + 44x - 168 = 0
4(x - 3)(x + 14) = 0
The solutions are 3 and -14, but only 3 makes sense in the story problem.