try something like this. the trick is position you can put the div wherever you want.
read something here. and you can read about hover here
here is an html example. (copy this to a text file and open it withyour browser)
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
<title>Test</title>
<script text="text/javascript"
src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.0/jquery.js">
</script>
</head>
<body>
<ul>
<li class="">Lynx</li>
<li>Jaguar</li>
</ul>
<div id="picture" style="position:absolute; top:0px; right:0px;">
</div>
<script type="text/javascript">
var animal = {
"Lynx":
"http://wnbaoutsiders.files.wordpress.com/2009/06/lynx21.jpg",
"Jaguar" :
"http://www.tropical-rainforest-animals.com/image-files/jaguar.jpg"
}
var hovered = function(e) {
//you can get what to show from the elemnt, instead of the content
// you could use an id.
var name = $(e.target).html()
$('#picture').append("<img src='" + animal[name] +"'/>")
}
var unhovered = function() {
$('#picture').empty();
}
//here you bind mouseenter and mouseleave
$('li').hover(hovered, unhovered);
</script>
</body>