In order to find the slop it is probably best to put the equation in y=mx+b form. This means to get y by itself on one side.
24x-9y=63 will then become -9y=63-24x in which y has been isolated.
Then you should divided by -9 to get the final form: y=24x/9 -63/9.
Now you can get the slope of the perpendicular line by taking the slope of the original equation and finding its reciprocal which is -9/24x. This is your answer.