Вариант ...
<!DOCTYPE html>
<html>
<head>
<title> title</title>
<script>
function fn(b) {
var a = "AB";
a = a.split("");
for (i = 0; i < a.length; i++) document.getElementById(a[i]).style.display = a[i] == b ? "" : "none"
};
</script>
</head>
<body>
<form method="post" action="">
<select id="my_select" onchange="fn(this.value);" >
<option value="">change</option>
<option value="A">A</option>
<option value="B">B</option>
</select>
<div id='container'>
<select id="A" style="display:none">
<option value="1">1</option>
<option value="2">2</option>
</select>
<select id="B" style="display:none">
<option value="11">11</option>
<option value="12">12</option>
</select>
</div>
</form>
</body>
</html>