After finishing all of the tasks required to begin crafting the Rocket Drill, Emmett will ask you to mix the rocket fuel while he argues with his father as a distraction. Pay attention to Doc's cues as he is yelling at his father to tell you what to do. The words will have extra emphasis on them, young Emmett will say them louder, and they will also appear all in capital letters if subtitles are enabled. There are 4 different sections to the sequence, Emmett will appear downstairs and will inform you when you have reached 25%, 50%, and 75% of the concoction. The commands get faster and faster as you progress. Unfortunately, the order of devices used is random each time so I cannot write you a step by step for this, just pay attention and react quickly. The meter will be shown and it will ding every time you get one cue correct.
Beware, about half way through Emmett's father will begin to yell similar words which will also appear in the subtitles, so you need to be extra careful that you only listen to Emmett's commands. If you mess up, you will know because Emmett will stop arguing with his father and come down to speak to you and tell you to listen for his cues. Should this happen to you, you can press the button and exit to the XMB and restart the game. Now you can load, which will start you back at the beginning from the mixing sequence and you may try again. Alternatively, as DarkSeraphim666 so graciously pointed out, you can simply press and load from there.
The cues will follow the lines of:
Sprinkle Bacteria Food:
Release Gaseous Pressure:
-Bags of Gas
Turn Electrical Crank: