Scroll a little less than half way down template "search_input_post" and find and modify this code:
<div class="blockrow">
<label for="forumchoice">{vb:rawphrase search_in_forums}:</label>
<ul class="multifield stacked group">
<li>
<select class="primary" id="forumchoice" style="width:500px;" name="forumchoice[]" multiple="multiple" tabindex="1" size="20">
{vb:raw search_forum_options}
</select>
</li>
<li>
<label for="cb_childforums" class="rightcol">
<input id="cb_childforums" type="checkbox" value="1" name="childforums" tabindex="1" {vb:raw childforumschecked} />
{vb:rawphrase also_search_in_child_forums}
</label>
</li>
</ul>
</div>
The size attribute determines the height