You can handle it in javascript itselt.
Try
Markup Code:
<asp:RadioButtonList ID="Radiobuttonlist6" runat="server"
RepeatDirection="Vertical" AutoPostBack="true" onclick="Validate('Radiobuttonlist6','Panel1')" style=" margin-left:10px; margin-top:44px" >
<asp:ListItem Text="this" Value="this"></asp:ListItem>
<asp:ListItem Text="this" Value="that"></asp:ListItem>
</asp:RadioButtonList>
JS function :
function Validate(rb, panel1)
{
var rb = document.getElementById('rb');
var panel = document.getElementById('Panel1');
var rblist = rb.getElementsByTagName("input");
for (var i = 0; i < rblist.length; i++)
{
if (rblist[i].checked)
{
if (rblist[i].value == "this")
{
panel.style.display = "block";
}
else if (options[i].value == "that")
{
panel.style.display = "none";
}
}
}
}
Try and revert
Hope this helps...