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<li><a class="qmparent" href="javascript:void(0)"><img class="qm-is qm-ia" src="Products.png" width="107" height="45" onmouseover = this.src="ProductsMouseOver.png" width="107" height="45"></a><ul>
<li><span class="qmtitle" >Main Products</span></li>
<li><a href="javascript:void(0)">60m</a></li>
<li><a href="javascript:void(0)">150m</a></li>
<li><a href="javascript:void(0)">600m</a></li>
<li><a href="javascript:void(0)">Technical specifications</a></li>
<li><a href="javascript:void(0)">Backpack with semi</a></li>
<li><a href="javascript:void(0)">Backpack with closed</a></li>
<li><a href="javascript:void(0);">Mouthpiece</a></li>
<li><a href="javascript:void(0);">Regulator</a></li>
<li><a href="javascript:void(0);">Monitoring</a></li>
<li><a href="javascript:void(0);">Buying a system</a></li>
</ul></li>
First, you might consider using CSS instead of all the JS, for the mouse-overs, and limit the JS to any onClick actions you require. The following is just based on observation of what you've posted.
<a class="qmparent" href="javascript:void(0)"><img class="qm-is qm-ia" src="Products.png" width="107" height="45" onmouseover = this.src="ProductsMouseOver.png" width="107" height="45"></a>
To start, the image won't inherently react to mouseover (reliably.) You want to mouseover the anchor:
<a class="qmparent" href="javascript:void(0)" onmouseover="document.getElementById('unique-id-here').src='ProductsMouseOver.png'"><img class="qm-is qm-ia" id="unique-id-here" src="Products.png" width="107" height="45" width="107" height="45"></a>
(Changes noted below for quoting)
Second, never do this:
href="javascript:void(0)"
Because if JS is disabled, the links won't work. What you want there is on click, return false, which tells the browser to allow JS to manage the navigation and not navigate to whatever is in the href. So if JS is disabled, the link will still work.
<a class="qmparent" href="file.html" onmouseover="document.getElementById('unique-id-here').src='ProductsMouseOver.png'" onClick="some_js_function('file.html'); return false;"><img class="qm-is qm-ia" id="unique-id-here" src="Products.png" width="107" height="45" width="107" height="45"></a>
third, no spaces in attributes (minor point, but will kick validation errors;) also in your original you have an incorrect quoting, the " should immediately follow the =:
onmouseover = this.src="ProductsMouseOver.png"
S/B
onmouseover="this.src='ProductsMouseOver.png'"
incorrect per point 1
Last, once you sort all this out, search this forum for ways to attach behaviors to elements so all this JS is extracted to external files or in the document head.
<li><a class="qmparent" href="file.html" onmouseover="document.getElementById('Products-hover').src='ProductsMouseOver.png'" onClick="some_js_function('home.html'); return false;"><img class="qm-is qm-ia" id="Products-regular" src="Products.png" width="107" height="45" width="107" height="45"></a>