It's not an easy puzzle, but basically, go here:
Set the game to a 3x3 set.
Set it to two colors
Go back into the game and stand on the big turret, facing the towers. Here's an example:
X X X
X X X
X X X
(y = the turret, ignore the dashes, its only for spacing on this board)
Now you have to look at the towers and see which ones are ON (the screens should be yellow). Depending on what you've been hitting on and off, it will be different for each player.
So here's a legend:
O = OFF
I = ON
Lets say a few towers are ON and it looks like this:
O I O
O O I
O O I
Make a note of which towers are ON... not off - ON. Then ALT-TAB back to the Lights out Game in your browser, and set the game like that. Blue means on, Red means off. Click the edit button so you can click on a colored spot and change it.
So you'd have 3 blue squares and 6 red ones, right? After this, you hit PLAY on the game - and then hit SOLVE. you MUST hit play first, or it wont work from what the video on youtube said.
It will give you a diagram telling you how many moves you need to make on each tower. Usually, it will be a single move on a few different towers. Once you have your solution (make a drawing and write it down) ALT-TAB back into TOR, and go to the towers that the java game told you to go to, and hit them whatever amount of times the game's solution tells you to hit them.
Once that happens, the turret should self activate. After this, right near the turret in a pool of green liquid, there should be a ship. Go into the ship and access the blue part and you should complete the mission.