Below is the core JavaScript you need to write:
<html>
<head>
<script type="text/javascript">
function CheckColors(val){
var element=document.getElementById('color');
if(val=='pick a color'||val=='others')
element.style.display='block';
else
element.style.display='none';
}
</script>
</head>
<body>
<select name="color" onchange='CheckColors(this.value);'>
<option>pick a color</option>
<option value="red">RED</option>
<option value="blue">BLUE</option>
<option value="others">others</option>
</select>
<input type="text" name="color" id="color" style='display:none;'/>
</body>
</html>