When your in young Emmetts lab he will be arguing with his father and you will have to use the machines as he says to. He drops hints so I recommend turning subtitles on and the keywords you have to listen for will appear in all caps. About halfway through is father will start using keywords as well ignore them and only focus on Emmett.
If you mess it up just reload the autosave either by pressing select and choosing load or go back to the XMB and reload up the game and it will load up when you first enter his lab.
The solution for this is random, it changes each time, so I can only provide you with keywords and what they mean:
Sprinkle Bacteria Food:
Release Gaseous Pressure:
-Bags of Gas
Turn Electrical Crank:
If you've done it right you will get the trophy when your using the drill on the jail wall.