Your objective is to place some diagonal 'mirrors' into the grid.
If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.
Each row and each column will contain exactly two
of the diagonal mirrors.