This extension displays your categories with their respective images, category is also displayed below the image with the number of products in the category.

Other versions are available that don’t have the category names and have better css, check out my other extensions here:

This extension installs like any other basic extension, there are instructions in the ReadMe.md and ReadMe.txt files in the zip file

Now add the extension to any page you like.

No files will be overwritten.