This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
A tan zhekran was a Romulan puzzle box. It required patience to solve; an individual had to use their fingers to move the panels on the box's sides into place, while also feeling its movements and listening to its internal mechanisms. According to Narek, the key to opening it was "taking the time to understand what is keeping it closed." Once the puzzle was solved, it would slowly open to reveal a small prize hidden inside.
Narek liked to use tan zhekran as personal thinking aids, much to the annoyance of his less-patient sister. Upon the completion of his mission in 2399, Narek attempted to kill Soji Asha by locking her in a Zhal Makh chamber with a tan zhekran that released a deadly radioactive gas when it was opened. (PIC: "The Impossible Box")