Hi,
I see you use the Categories Images plugin. For that to work, a small custom snippet is needed to be placed into the functions.php file in your active theme directory:
1. Make sure you have a back-up of everything
2. Place the following code to the functions.php file in your acrive theme directory (copy from line 3 only!):
3. Save the file, and you are done.
After this, category images should start showing up. If you need help with the implementation, feel free to leave FTP details and I will do it for you.