[cloayza]

Podrias usar el siguiente código

Código Delphi [-]
procedure TForm1.Button1Click(Sender: TObject);
var 
    i, CountX, CountV:Integer;
begin
       CountX:=0; CountV:=0;
      for i:=0 To ListView1.Items.Count-1 do
      begin
             if ListView1.Items[i].Caption='X' then
                Inc(CountX);
             if ListView1.Items[i].Caption='V' then
                Inc(CountV);
      end;
      
     ShowMessage(Format('Conteo de X: %d Conteo de V:%d',[CountX, CountY]));
end;

Saludos