In answer to your actual question a paragraph cannot contain any other block elements, which includes tables. Also in addition to this the closing </p>
tag is optional so the first closing tag that is subsequently found by the parser will deem to have closed the paragraph.
It would help if I could see more of the code and layout, however I believe that removing the <p>
tags from around the tables and then correctly formatting the positioning of your tables using CSS should achieve your results.
<div class="right_articles">
<table>
<tr>
<td>
<img alt="Img not found" src="images/ribbon.gif"
style="width: 155px; height: 125px;" />
</td>
<td>
<asp:Label ID="Label1" runat="server" Text="Label"></asp:Label><br />
<asp:Label ID="Label2" runat="server" Text="Label"></asp:Label><br />
<asp:Label ID="Label3" runat="server" Text="Label"></asp:Label>
</td>
</tr>
</table>
<p> </p>
<table>
<tr>
<td>
<img alt="Img not found" src="images/medal.gif"
style="width: 155px; height: 125px;" />
</td>
<td>
<asp:Label ID="Label4" runat="server" Text="Label"></asp:Label><br />
<asp:Label ID="Label5" runat="server" Text="Label"></asp:Label><br />
<asp:Label ID="Label6" runat="server" Text="Label"></asp:Label>
</td>
</tr>
</table>
</div>