I'm not following you here.
First, thanks for the first picture! I've got to order that ball hitch kit from Northern Tool ($55, search "great day lawnpro" on their site) for my own garden tractor so I can tow small utility trailers around the place.
Second, the picture of the rack that you show has a receiver hitch mounting, which your lawn tractor doesn't have. You could use that carrier, but you are going to need to add some additional bracing down to the back of the lawn tractor in order to support a sprayer - assuming you put a 15-gallon sprayer on there, you're looking at the weight of that carrier, the sprayer weight, plus 120 pounds of liquid.