Advantage or Disadvantage?

Mate in 4

This is in no way a mate-in-four. You can't just post the end of a game you played, or some random sequence of moves, and have people try to solve it. Black did not play the best defense on every move, therefore the puzzle is 'flawed.'

It is easy for white to win material here. For example:

1.Nxf6 Rxg4  2.Nd7+ Ka7  3.Ra1 

"White to play and win" would be a better title, because there's no way to force mate in four, five, or even eight moves with accurate defense.

The puzzle is not flawed however with the right move the mate can need more than 4 moves.

Black did not play stupid moves. If he didn't eat the knight then 1. Nd7+ ... Ka7 or ka8  2. Ra1 and the next move will be Rxa2# with no way of stopping it. If Qxa1 then Rxa1# If 1....Qa7 or Qa6 then 2.Rxa7 or Rxa6 2... Kxa7 or Ka8 3.  Ra1#

In this puzzle the queen sac was needed for the same reason.  If Qxa1 then Rxa1# If 1....Qa7 or Qa6 then 2.Rxa7 or Rxa6 2... Kxa7 or Ka8 3.  Ra1#

Another interesting variation is after  2. Bxd6+ Ka7 3. Ra1 b5 (opening a way to escape for the king 4. Rxa2+ Kb6 (trying to escape) 5. Bc7#

There is no accurate defence. Even the queen sac on 1...Qxb1 loses to 2.Nd7+ 3. Ka7 Rxb1 and next move is the unstoppable Ra1#.

 My favorite one is this one:

After 1. Nxf6 Ka7 2. Ra1 (pinning the queen) Ka6 (thinking of Kb5 and escaping) 3. Be2!! Ka7 (forced to go back into his own trap) 3. Rxa2#

"In this puzzle the queen sac was needed for the same reason.  If Qxa1 then Rxa1# If 1....Qa7 or Qa6 then 2.Rxa7 or Rxa6 2... Kxa7 or Ka8 3.  Ra1# There is no accurate defence."

There is an accurate defense against mate... but you missed it. Instead 3...Qxa1 , there's 3...Qa5! 4.Rxa5 bxa5 White's up a piece for a pawn but a long way from mate. So the title of the puzzle "Mate in 4" is incorrect and it should be "White to play and win."

 That's right. that looks like a good defence but black is holding by a thread. After Bb4, The queen is lost for a bishop and white two rooks are closing in on the king. White next move will be Be6 threatening the rook. Then Rxa5 and the king has to rely on his rook to stop Rc8# white is free to advance his passed d pawn who in turn will put pressure and on the c8 case and lead to victory.

 Which means that Qa5 is not the best move. I didn't analyze that one yet but Qa6 might be the best bet.

It seems that in any case it is a win for white. The title is indeed inacurate. 

 The puzzle is flawed, because it claims 'Mate in four.' Eating the knight was not a bad move, as I showed with my variation, that you quoted here without recognition...ahem (where white gets Queen for rook after 2.Nd7+). The only flawed move was the blunder 3...Qxa1, giving white mate. Likeforests pointed out the correct move of 3...Qa5, which shows that white cannot force a quick mate. This would of course be 3...Qa6 in my variation, which works just as well.