I have never worked on lawnmowers before, but to me it looks like yes, the pulley would mount in the 2nd hole on the middle thingy, which would appear to be a belt tensioner. It looks like that whole assembly, with the two pulleys on it, would rotate in one direction and be spring-loaded in the other. So basically you install the new pulley, rotate the tensioner so that it is perpindicular to the two main pulleys (forming a cross shape with all 4 pulleys) and then run the belt across the two main pulleys, in such a way that it runs between the two smaller pulleys. It might help to have another person to help you do this. Once the belt is in place, release the tensioner and the two small middle pulleys will swivel into place and keep it taut.