I will skip the observation part. Remember what we should observe:
- brief survey
- check every square around the King
- search for all checks
- guess why each black piece is on the board
If you try to check on your first move, it's 99.999% wrong. The first move is actually a quite move Kf8, preparing to checkmate (double check) with Rf4#.
Now there are couple of defense.
g5+, you should not go Rg7+, because Bf7 will block your check. But Bg7#
Bxf7, of course Bxf7#
xc3 or Bxf3, Rf4# is still mate.
Kb3, Na5#. This is tricky one. Discovered checks are no longer working because black can block.
Now why each piece is on board?
Black a2, a4, b4 Pawns, they will block the King when Na5#
Black d7 Pawn, stops the Knight check.
Black b8 Knight, prevents Kd8 or Kxd7.
Black g7 Pawn, lets King moves to f8 without check.
White Pawn on d6, stops black d5 blocking the c4-g8 diagonal.
White Rook on f3, defends c3 Bishop if Bxc1 .
White Pawn on e2, guards d3 square if Bxf3.
Other pieces are obvious useful.