Say pieces on a board, make each a pair with another piece.
so figure out how a piece can move.
pick any piece, try to move it somewhere.
when you move a piece you have to move it's pair at the same time.
when you move to a piece it's pair has to move at the same time too.
a piece always becomes a pair with the piece it moves to.
no matter how many pairs, there's only one answer to how a piece can move.
A common problem type, I forget what it's called.
There's only one answer for how any piece can move.
A piece always goes where a piece leaves.
You can't move a piece that moves where the piece came from.
No such thing as a free space, a piece always moves to another piece.
A pair never moves to a pair.
A piece works out to move where another piece can get back to where a piece moves from.
so try this...
draw starting at each piece a line that shows the piece it moves to, and each piece to move for how a piece moves back
where it starts.
see this as a machine diagram.
move a piece then figure the machine diagram again, it's the same machine though...
see how every other piece moves another way now?
what happened for how the machine moved?