technically....you don't even need that line in your header.php unless you really want it there....just a personal thing, but I hate css in a css file and inline in a php file.
You could delete the line from header.php and in your style.css change
background: #777;
to
background: #777 url('images/holly2.JPG') repeat fixed;
if you wanna keep it in header.php,
body{ background: #fff url("<?php bloginfo('template_directory'); ?>/images/holly2.JPG") repeat fixed;
should work fine. I do know this code works as I copied it from my theme, with a fixed background.
After you make the changes to any css, press ctrl+f5 while looking at your site to refresh the cache and see changes
(also, I assumed you wanted your image to tile horizontally and vertically, if not deleted/adjust the repeat)