Clearly, even if white stopped the black b pawn from queening e.g. Re1, black has enormous winning chances by advancing the d pawn. So the solution is obvious, very active attack. Now there looks like a routine win here with either Re8 or Nf6 but Re8 wins, Nf6 loses.
If 1. Re8, threatening 2. Nf6 and 3. Mate, (Black cannot advance 1.…f3 or f4 clearing f2 for the king. But then 2. g5*f3 Kf7 3. Re7+ Kh8 4. f8=Q#) so black must play 1. … Rh4 (and if 2. Nf6 then Rh8) so 2. Rb8 Rh8, 3.R*b3 Ra8 (for example), 4. Rd3, Ra5 5. Nf6 d4 6.f4 Ra4 7. Kf3, 8. Ke4, 9. R or K *d4 wins.
However, 1. Nf6 first loses as 1.… Rb8, 2. f4 (to clear Rh3,then Rh7 but black can move then 2. … b7 3. Rh3 b8 (Q) So 1. Nf6 is incorrect and white must play 1. Re8 to win.
White must stop the pawn was my first thought, but then I noticed a stronger threat that wins the exchange:
1. Re8! b2 (alternatives below) 2. Nf6!
And Rg8# can’t be stopped, only delayed. So, black must find alternative moves at move 1:
1. Re8 Rf4 2. Nf6 Rf6 (forced) 3. gf6 Kf6 4. Rb8 d4 5. Rb3 Ke5 6. Kf2 Kd5 7. Ke2 Ke5 8. Rb5 Kf4 9. Rd5 will win with ease. In this ending, it really isn’t possible for black to support the d-pawn while, at the same time, advancing the kingside pawns.
At move 1, black could try Rh4-Rh8 and exchange rooks if white persists with Ng6:
And I don’t know if white can win this. White will be able to move the knight between b1 and c3/a3/d2 whenever he needs to make black move next, but this might not be enough. However, white need not allow this iffy ending:
1. Re8 Rh4 2. Rb8! and the b-pawn falls, and with it pretty much all black’s counterplay.
1. Re8 b2 2. Nf6+-; 1…Rb6 2. Nxb6 b2 3. Re1; 1…f5 2. exf6+ Kh7 (2…Kf7 3. Re7+ Kg8 4. f7+-) 3. f7 +-
-knighk
Clearly, even if white stopped the black b pawn from queening e.g. Re1, black has enormous winning chances by advancing the d pawn. So the solution is obvious, very active attack. Now there looks like a routine win here with either Re8 or Nf6 but Re8 wins, Nf6 loses.
If 1. Re8, threatening 2. Nf6 and 3. Mate, (Black cannot advance 1.…f3 or f4 clearing f2 for the king. But then 2. g5*f3 Kf7 3. Re7+ Kh8 4. f8=Q#) so black must play
1. … Rh4 (and if 2. Nf6 then Rh8) so 2. Rb8 Rh8, 3.R*b3 Ra8 (for example), 4. Rd3, Ra5 5. Nf6 d4 6.f4 Ra4 7. Kf3, 8. Ke4, 9. R or K *d4 wins.
However, 1. Nf6 first loses as 1.… Rb8, 2. f4 (to clear Rh3,then Rh7 but black can move then 2. … b7 3. Rh3 b8 (Q) So 1. Nf6 is incorrect and white must play 1. Re8 to win.
Psyche
White must stop the pawn was my first thought, but then I noticed a stronger threat that wins the exchange:
1. Re8! b2 (alternatives below)
2. Nf6!
And Rg8# can’t be stopped, only delayed. So, black must find alternative moves at move 1:
1. Re8 Rf4
2. Nf6 Rf6 (forced)
3. gf6 Kf6
4. Rb8 d4
5. Rb3 Ke5
6. Kf2 Kd5
7. Ke2 Ke5
8. Rb5 Kf4
9. Rd5 will win with ease. In this ending, it really isn’t possible for black to support the d-pawn while, at the same time, advancing the kingside pawns.
At move 1, black could try Rh4-Rh8 and exchange rooks if white persists with Ng6:
1. Re8 Rh4
2. Nf6 Rh8
3. Rh8 Kh8
4. Nd5 b2
5. Nc3 Kg7
And I don’t know if white can win this. White will be able to move the knight between b1 and c3/a3/d2 whenever he needs to make black move next, but this might not be enough. However, white need not allow this iffy ending:
1. Re8 Rh4
2. Rb8! and the b-pawn falls, and with it pretty much all black’s counterplay.
1.Re8 Rh4
(1…b2 2.Nf6 Rb8
(2…Rh4 3.Rg8#)
3.Rxb8 b1=Q 4.Rxb1 Kf8)
2.Rb8 d4 3.Rxb3 Rh8 4.Rd3 Rc8 5.Rxd4 Rc2+ 6.Kg3 Rc7 7.Nf6 Rc5 8.f4 Rc3+ 9.Kg4 Rc8 10.Nd7 Rd8 11.Kf3 Ra8 12.Ne5 Ra3+ 13.Ke4 f5+ 14.Kd5 Ra6 15.Rc4 Rb6 16.Rc7+ Kh8 17.Rc6 Rb1 18.Rxg6 Ra1 19.Ke6 Ra8 20.Kxf5