Try
<asp:DropDownList ID="ddlMonths" runat="server" AutoPostBack ="true" OnSelectedIndexChanged ="Month_Changed">
<asp:ListItem Text ="Please select" Value ="0"></asp:ListItem>
<asp:ListItem Text ="January" Value ="1"></asp:ListItem>
<asp:ListItem Text ="February" Value ="2"></asp:ListItem>
<asp:ListItem Text ="March" Value ="3"></asp:ListItem>
<asp:ListItem Text ="April" Value ="4"></asp:ListItem>
<asp:ListItem Text ="May" Value ="5"></asp:ListItem>
<asp:ListItem Text ="June" Value ="6"></asp:ListItem>
<asp:ListItem Text ="July" Value ="7"></asp:ListItem>
<asp:ListItem Text ="August" Value ="8"></asp:ListItem>
<asp:ListItem Text ="September" Value ="9"></asp:ListItem>
<asp:ListItem Text ="October" Value ="10"></asp:ListItem>
<asp:ListItem Text ="November" Value ="11"></asp:ListItem>
<asp:ListItem Text ="December" Value ="12"></asp:ListItem>
</asp:DropDownList>
<br />
<asp:TextBox ID="txtMonths" runat="server"></asp:TextBox>
Protected Sub Month_Changed(sender As Object, e As EventArgs)
Dim month As Integer = Integer.Parse(ddlMonths.SelectedItem.Value)
txtMonths.Text = DateTime.DaysInMonth(DateTime.Now.Year, month).ToString()
End Sub