I set up a sub-domain, using CPanel, and have uploaded php pages.  The subdomain has one directory called "pics" into which I have placed the images used by the site pages.  When I access the subdomain www.SUB.my-domain-name.org the index.php loads correctly but none of the graphics display.  This suggests the subdomain can be found via DNS.  When I right-click on a missing image and look at the properties for the missing graphic  I see http://www.SUB.my-domain-name.org/pics/graphic.jpg.  This looks correct to me because a file called graphic.jpg resides in the directory called pics.

If I access using the URL  www.my-domain-name.org/SUB/ everything works fine. 

What can I do to make this work.  Another sub-domain on the site is working fine and the directories are accessable as expected.

Add the subdomain in question to your Hotlink Protection in the public_html .htaccess file.