Say pieces on a board, make each a pair with another piece.

like...

|55|33|66|
|44|66|55|
|33|44|22|
|22|11|11|

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?