The position evaluates as mate in two, but it appears that white can do a mate in one. Presumably the white king hinders the mate in some way so that mate in one is not possible.

White appears to have two different mate in ones; the white king should interfere with both of them. Consider where the lines of the two different mating attacks intersect.

The king is on e5, interfering with both the bishop guarding g7 and the rook reaching e8. The winning move is Ke5-d6; black can stop one or the other threatened mate, but not both.

One subtlety that I had overlooked when I first set this problem is that another way white could be delayed is if the white king is in check; then the first move could be escaping check and so renewing a mate threat for the second turn. To prevent such solutions I have adjusted the board so that wherever the white king goes it can be harried with further checks, except on the three squares a3, d1, and d6. Neither a3 nor d1 can be reached from an adjacent square where the white king is in check. d6 can be reached from either c6 or e6, but in neither of those positions would the position be valid, as there is an impossible double (or triple) check. Some additional casework is required to show that capturing a checking piece does not work either.

There are many different mate in ones being threatened. For the position to be mate in two, something must be going on that makes none of those moves legal.

Did you read the solution to problem 1?

The white king must be in check, and needs to find a square from which it cannot be checked again.

The king is on b5, and the move is Kb5-a6.

The black pieces attack only white squares, so the king is on a white square. The black bishop can attack any white square in one move except a6, h7, or the 8th rank, and the knights likewise every black square except h8.

The puzzle is completely symmetric except for the extra file on the right side, so this extra file must be involved in some way for the solution to be unique. I intended people to search for solutions where the king started on this file or moved to this file, but no such solution works. Instead the file is important by its absence on the left side; the bishop cannot attack a6 because that would require going off the board. On the mirror side, if the king were to go to g6, the bishop could attack it from h5.

The white knight on d3 is necessary to block the black bishop from attacking a6 from e2. I think the white knight on d5 is only for aesthetic reasons. The white bishop is needed to stop the black pawn advancing and giving the black king a flight square.

King on c2 or e2 and taking d1 is not a solution because the initial position would be an impossible double check.