Why so elusive; it appears so mild, ordinary.

Mate in 9, 8 or even 7 isn't hard to find, but how to trim it down to 6? Here is a big clue: these longer combos all have BK running to the border for mate. The #6 solution gets it done board central!

The first move is important, and perhaps not hard to get, but how to spot it as the right one? Only by being aware of the rest, apparently...

To become aware, BK throughout is confined to 3 squares: e5, f5 & f4, from whence derives the mid-board #6 mate. Visualizing this confinement evokes a synthesis of this mating concept, greatly simplifying the problem. E.g., your d3K, g6R & g2P have power ranges that define BK's confinement, with d5 being the only escape square, plugged by the Bishop!

R never moves, WK trails behind BK, B traps him, and P nails him.

Finally, this B only occupies d5 when going in for the trap.

1. Bf7 ~ clears rank 6 for R, and prepares for Bd5 later!
1...Ke5 ~ if Kf5, #5 as below...
2. Ke3...Kf5 (forced)
3. Kd4...Kf4 (forced)
4. Bd5 (there it is!)...Kf5 (forced)
5. Be4+ (prime position)...Kf4 (forced)
6. g3#

This same position, Black to move, without the Pawn, and the board edge @ g-file instead of the Rook, would be stalemate. Black is entirely confined. But as you see, he was given no choice, since each move is forced; even his first move!

If 1...Kf5 (the only other option), then 2. Kd4...Kf4 (forced), etc , and it's #5, not #6.

Thank you, sirisaac, for a wonderful contribution! 😊
3 stars ⭐ ⭐ ⭐

In my previous Comment, I had 2. Bf7...Kf5 (forced). Well, it's not forced, as 2...Kf4 is an alternative.

Furthermore, if 2...Kf4, a nuance is required of W to avoid stalemate. [Remember, this studys Black moving first, with 1...Ke5 (forced).]

2. Bf7...Kf4
3. Kd4...Kf5
4. Bd5...Kf4
5. Bc6 (*waiting move*)...Kf5
6. Be3+...Kf4
7. g3#

Note: this (7. g3#) is White's 6th move, since his first move (2. Bf7) was a reply to Black's 1...Ke5.

5. Bc6 is a *waiting move* because, if 5. Be3 (no check), Black would have nowhere to move, thus, stalemate. This waiting move puts Black into zugswang again, his only move available being the one which W needs him to make, so W can put him in check, penultimate to checkmate.