<style>
img:hover,img.hovered {border: 5px red solid;}
</style>
<ul>
<li id="hover-over-me">Dogs</li>
</ul>
<img src="http://4.bp.blogspot.com/_7VyEDKFMA2U/TOX9ZL7KRPI/AAAAAAAAACM/-XSoYjePBPk/s1600/cute-puppy-dog-wallpapers.jpg" />
<script>
$("li").mouseenter(function(){
$("img").addClass('hovered');
});
$("li").mouseout(function(){
$("img").removeClass('hovered');
});
</script>