Daillyn,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
dd.box_first{
background-color: #FF0000;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(function() {
$( "[data-cls]" ).each(function() {
var el = $(this), cls = el.data("cls");
el.next().addClass(cls)
});
});
</script>
</head>
<body>
<dt class="box_first box__open" data-cls="box_first">
<img src="" alt="">
<h2>text</h2>
</dt>
<dd class="box__hide"><p class="hidden_text">text</p></dd>
<dt class="box_first box__open" data-cls="box_first">
<img src="" alt="">
<h2>text</h2>
</dt>
<dd class="box__hide"><p class="hidden_text">text</p></dd>
</body>
</html>