Why is <table> not allowed inside <p>
In HTML it's important to understand that P elements cannot contain other block level elements and TABLE is a block level element. The P closing tag is optional and when you try to make a P element contain something that it cannot contain, the closing P tag is assumed by the browser.
The P element represents a paragraph. It cannot contain block-level elements (including P itself).
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>