It looks like your spindle has a male thead on it, and its held on with nuts. There was also one that has a female thead on the spindle and it used bolts. Make sure the tool you get is sutable* for male threaded spindles, as some of them wont fit.
*the "pushing" part of the tool needs to be able to screw back enough to alow the spindle to go up inside the outer part of the tool. Some only wind out flush with the outer thead part (I hope that made sence)