A rook is promoted to an empress, moving like a rook or a knight, a bishop to a queen, and a knight to a princess, moving like a knight or a bishop. They are not only promoted but also demoted, switched between two levels again and again with certain rules.
If one of your knights on the board is self-captured, then the knight on the board is immediately promoted to a princess. The princess is demoted to a knight as soon as the self-captured knight is dropped onto the board. If both of your knights are self-captured, then one of them is dropped with a princess power and keeps it until the other knight is dropped. However, when one of your knights is captured by an enemy piece, the on-board knight is not promoted.
Accordingly, a knight on the board, the other on the airfield, then the on-board knight keeps promoted.
Suppose one of your knights is captured by your opponent, the other is on the board, and your opponent's two knights are on the board. If you capture one of your opponent's knights, then by the rule of SC-chess, you and your opponent's knights are exchanged and go to their airfields. Hence on-board knights are immediately promoted, not only yours but also your opponent's.
Promotion rules for a rook and a bishop are very similar.
[Solution]: Pg8=Q+ Kxg8 Nxf6 Kh8 B+xe6 Q*g7 B+g8.
Just after Nxf6, the white bishop d7 is promoted to a queen (denoted by B+). By B+xe6, white captures a black knight, and so imprisoned black and white knights are exchanged immediately, that promotes the on-board black and white knights to princesses. Q*g7 means that a queen is dropped onto g7.
The promotion rules themselves make a game more difficult and interesting, because the two states "one promoted piece" and "two unpromoted pieces" are well-balanced and an advantageous choice depends on the situation.