Engage,
You did it right and it should show up in the Mission Editor.
In the Mission Editor, click on the Payload icon, then on Paint Scheme and there you should my Livery, 10th_TFW_Vultures_Europe1_by_Toby.
If that doesn't work, check the graphics.cfg again. If you missed one quote or comma, it won't show up. And check that you copied the description.lua file, in the folder 10th_TFW_Vultures_Europe1_by_Toby, to the correct destination i.e. \DCS A-10C\Bazar\Liveries\A-10C
Good luck