Ok, here you go.
In your navbar template
FIND
Code:
<if condition="is_array($navbits)">
ADD ABOVE
Code:
<!-- peterska2 navbar box edit -->
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td align="left">
<!-- / peterska2 navbar box edit -->
FIND
Code:
<else />
<div class="navbar" style="font-size:10pt"><a href="$vboptions[forumhome].php$session[sessionurl_q]" accesskey="1"><img class="inlineimg" src="$stylevar[imgdir_misc]/navbits_start.gif" alt="" border="0" /></a> <strong>$vboptions[bbtitle]</strong></div>
</if>
ADD BELOW
Code:
<!-- peterska2 navbar box edit-->
</td>
<td align="right" width="22%" class="alt1">
<table cellpadding="1" cellspacing="1" border="0" align="right">
<tr>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="$vboptions[bburl]">Forum</a>
</td>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="http://www.yahoo.com" target="_blank">Yahoo</a>
</td>
</tr>
<tr>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="$vboptions[homeurl]">Home</a></td>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="http://www.vbulletin.com" target="_blank">vBulletin</a>
</td>
</tr>
<tr>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="http://www.google.com" target="_blank">Google</a>
</td>
<td class="alt1">
<img src="http://www.el-halawa.net/forum/ambience/icons/icon2.gif" /> <a href="http://www.hotmail.com" target="blank">Hotmail</a>
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- / peterska2 navbar box edit -->
Save the template.
I've added the links as shown in your screenshot, if you want to change these you will need to change them manually in the template. You may need to adjust the table width (specified at 22%) to suit your site too.
The only thing it hasn't got is a box around it as it does not go right up to the members info box in the navbar.