<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>

    <div class="linktomouseover">
    <a class="nthn">link1</a>
</div>
<div class="linktomouseover2">
    <a class="test">link2</a>
</div>



    <script>

    jQuery(function() {
    jQuery('.linktomouseover').mouseover(function() {
        $(.linktomouseover2).css('background-image', "url('test.jpg')");
    });
});

    </script>

jQuery(function() {
    jQuery(".linktomouseover").mouseover(function() {
        jQuery(".linktomouseover2").css('background-image', "url('test.jpg')");
    });
});