Coaxing Refers to Bringing the Zybellum Shards (The floating star you get from a compression event) towards the Rock Analysis Lab. To do this you need to get the perk "Zybellium Mastery" Which automatically unlocks when you reach enough prestige points (The 2nd row on the right). Once you have this perk. A light will flicker on top of your Lab. Click the light when it is fully white 20 times. (You can do this even if there isn't a Zybellium currently floating in your game).