저도 잘은 모르지만..
이부분이 이상이 있는것 같습니다.

type TDate = record
    Day: Integer;
    Month: Integer;
    Year: Integer;
end;    <---// end가 빠져 있네요.

그리고요 type 부분이 implementation 밑에 있는것이 좋습니다.
즐프되세요.

implementation

type TDate = record
    Day: Integer;
    Month: Integer;
    Year: Integer;
end;

var
   OrderDate: TDate;

참고하십시요..


unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TDate = packed record
    Day: Integer;
    Month: Integer;
    Year: Integer;
  end;

type
  TForm1 = class(TForm)
    Button1: TButton;
    procedure Button1Click(Sender: TObject);


  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  OrderDate: TDate;

implementation

{$R *.dfm}

//버튼클릭시
procedure TForm1.Button1Click(Sender: TObject);
begin
  with OrderDate do
  begin
    if Month  = 12 then
    begin
      Month := 1;
      Year := Year + 1;
    end else
      Month := Month + 1;
  end;
end;

end.

답변감사드립니다(냉무)......정말로요......^^