There's literally "points" for capturing pieces. Every time you capture a black piece, you gain energy corresponding to that piece's chess point value. Pawns are worth one point, bishops and knights three points, and rooks five points. Notice that since all the black knights have the same moves as you, you will never be able to capture any black knights.
Since you only have one energy to start, there's only one possible first move you can make. And then since the last square is you capturing the king, what's the second to last square you need to go to? What piece is protecting that square? And what piece is protecting that piece's square?
It takes at least four hops for a knight to move two squares diagonally. That means that it takes at least five hops to go from the rightmost bishop to the king. If you only have four energy after capturing that bishop, you must have taken a wrong turn.
All rooks and bishops are captured by the time the white knight reaches the king, and you end your journey with exactly zero energy remaining.
Since you start and end your journey on the same color, you'll make an even number of total hops. But capturing all the rooks and bishops adds twenty-two total energy to your starting one energy for a total of twenty-three, an odd number. That means you'll have to capture a pawn somewhere along the way.
The pawn you need to capture is the b-file pawn, and you'll have to do it on your way to capturing the third bishop and second rook.