Custom events is the solution. Try to search for it in the search engine.
I would put your product category images is a List with a nice TileLayout or custom skin. Then you can use navigator.pushView(views.nextView,categoryList.selectedItem) to pass the selected image to the next view.
The tile list could have a custom skin or itemRenderer to make the images look however you'd like.
If your home page requires the images to be static (not in a list), then you could listen for a click event on each image, put the image id/fileName inside an object, then pass the object using pushView.
But, using a tile List for you images on the home page makes the most sense to me, but I don't know what your home view design is.
If I understand you correctly, you can pass data to the next view by passing the second parameter to the pushView method.
I've written similar apps in the past and found that a singleton class alleviates some of these issues. If you use a singleton to track currently selections all your views can access the same data without having to pass and return data from each other.
Hope this helps,