<p>Maybe this is an easy question, maybe not.  I have a select box where I hardcode with width. Say 120px.</p>

<p><div class="snippet" data-lang="js" data-hide="false" data-console="true" data-babel="false">
<div class="snippet-code">
<pre class="snippet-code-html lang-html prettyprint-override"><code>&lt;select style="width: 120px"&gt;
  &lt;option&gt;REALLY LONG TEXT, REALLY LONG TEXT, REALLY LONG TEXT&lt;/option&gt;
  &lt;option&gt;ABC&lt;/option&gt;
&lt;/select&gt;</code></pre>
</div>
</div>
</p>

<p>I want to be able to show the second option so that the user can see the full length of the text.</p>

<p>Like everything else.  This works fine in Firefox, but doesn't work with Internet Explorer6.</p>

If you have the option pre-existing in a fixed-with
```
<select>
```
, and you don't want to change the width programmatically, you could be out of luck unless you get a little creative.
You could try and set the
```
title
```
attribute to each option. This is non-standard HTML (if you care for this minor infraction here), but IE (and Firefox as well) will display the entire text in a mouse popup on mouse hover.
You could use JavaScript to show the text in some positioned DIV when the user selects something. IMHO this is the
not-so-nice
way to do it, because it requires JavaScript on to work at all, and it works only
after
something has been selected -  before there is a change in value no events fire for the select box.
You don't use a select box at all, but
implement its functionality using other markup and CSS
. Not my favorite but I wanted to mention it.
If you are adding a long option later through JavaScript, look here:
How to update HTML “select” box dynamically in IE