main.dart

class _MainPageState extends State<MainPage> with SingleTickerProviderStateMixin {
  int points = 0; //<-- add points field
  ...

  @override
  Widget build(BuildContext context) {
    return Material(
      child: Stack(
        fit: StackFit.passthrough,
        children: <Widget>[
          Image.asset(...),
          Row(...),
          _drawPoints(), //<-- add points widget on top of stack
        ],
      ),
    );
  }

  void _onTap(Note note) {
    setState(() {
      note.state = NoteState.tapped;
      ++points;            //<-- increase number of points
    });
  }
  
  _drawPoints() {          //<-- draw points
    return Align(
      alignment: Alignment.topCenter,
      child: Padding(
        padding: const EdgeInsets.only(top: 32.0),
        child: Text(
          "$points",
          style: TextStyle(color: Colors.red, fontSize: 60),
        ),
      ),
    );
  }
}