Hi,
Please refer below code.
HTML
<div>
    <script type="text/javascript">
        function ValidateMonth(sender, args) {
            var fromMonth = document.getElementById('ddlFromMonths').value;
            var toMonth = document.getElementById('ddlToMonths').value;
            args.IsValid = parseInt(toMonth) >= parseInt(fromMonth);
        }
    </script>
    From :
    <asp:DropDownList ID="ddlFromMonths" runat="server">
    </asp:DropDownList>
    To:
    <asp:DropDownList ID="ddlToMonths" runat="server">
    </asp:DropDownList>
    <asp:CustomValidator runat="server" Display="Dynamic" ErrorMessage="To month must be greter than from month"
        ClientValidationFunction="ValidateMonth" ForeColor="Red" ValidationGroup="val1"></asp:CustomValidator>
    <br />
    <asp:Button Text="Submit" runat="server" ValidationGroup="val1" />
</div>
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        PopulateMonths(ddlFromMonths);
        PopulateMonths(ddlToMonths);
    }
}
private void PopulateMonths(DropDownList dropDownList)
{
    var months = DateTimeFormatInfo.CurrentInfo.MonthNames.Select((m, i) => new { Month = m, Value = i + 1 }).Take(DateTimeFormatInfo.CurrentInfo.MonthNames.Length - 1);
    dropDownList.DataSource = months;
    dropDownList.DataTextField = "Month";
    dropDownList.DataValueField = "Value";
    dropDownList.DataBind();
}
Screenshot
