This position closely resembles the last one; but here each side has an extra piece, and the one that matters is White’s bishop on c7. Now if Black tries the same beginning move discussed in the prior position—Ng4—White has a better way than Rd1 to fend off the threat of Ra1#. He can instead play Bb6, preparing to meet Black's Ra1 with Bg1, which would effectively block the check. So Black needs another idea.
The natural alternative to explore is an immediate 1. …Ra1+, forcing White’s king to h2. Black then looks for his next check and finds 2. …Ng4+, forcing the king up another square to h3. Now watch this: Black plays 3. …Ne3—not a check, but renewing the threat of mate via Rh1 since the knight now seals off g4 and keeps the White king trapped on the h file. White somehow has to find an out for his king. Moving it to h4 won’t do; that still leaves no safe square after Black plays Rh1. But White has two other choices.
(a) The first is Kh2, readying the king to capture the rook if it moves to h1. But keep track of the Black knight’s position: it has moved twice and is on e3, a dark square. If White does move his king to h2, another dark square, Black can skip Rh1; instead he wins a rook with the knight fork Nf1+.
(b) White’s other option in reply to 3. …Ne3 is to step his g3 pawn forward to g4, giving the king a flight square to the side. Now Black plays 4. Rh1 and White has 5. Kg3. Again, though, this puts White’s king onto a dark square and allows Black to win the rook with the knight fork Nf1+.
This whole sequence also was available in the previous position; if you saw it there, great. The point is that here you would have to use it. The shorter fork described in the previous frame no longer works. In a sense, though, the lesson of this position is the same as in the prior one: think about checks and mate threats you can create, not just on the board in front of you but also on the board as it will look after a check or two or after some other set of forcing moves. Here this means seeing 3. …Ne3, which doesn’t give check but does threaten mate and so forces White to choose between two moves that each lead him into a fork. When your knight is hopping around as Black's does here, you especially want to think about forking possibilities at every turn; 3. …Ne3 not only creates a mate threat but also puts the knight on a dark square along with White’s rook, meaning that Black can fork the rook if White’s king steps onto one of its available dark squares as well—as it soon must.