What expression is equivalent to x^2+2x-24/3x+18

By "x^2+2x-24/3x+18," I'm assuming that you meant

x^2+2x-(24/3)x+18.       Combine the x terms:  2x - 8x = -6.  I do not think this is the correct interpretation of your problem, so will work on the following instead:

x^2+2x-24/(3x+18)         Those parentheses make a huge difference.  You 
                                        cannot leave them out if you want to be understood 
                                         correctly.
                                             24                             8
Now we have    x^2 + 2x - = x^2 + 2x -
                                           3(x+6)                       x+6

Your pictures are upside down