First of all, in the second part of the puzzle, synergy's really important with your partner,  this's why I'd advise for you & your partner to decide who'll be the leader.
The leader'll be the one controlling the situation, guiding what the other teammate should do. I recommend the leader to be the one using the black code during the first part of the puzzle, while the teammate uses the yellow one. After entering their codes they'll each see panels that looks like these: 
  At the top of each panel there'll be some symbols, i'll call them a "code", the leader and his teammate should send a print to each other with the code in the top of their panels, these are the symbol the other person - be it the leader of the teammate - will be using during the resolution of the puzzle.
Example: 
So, here's how the puzzle works... Basically, you need to match 3 things correctly for the dots to light up, these things would be the following: The leader symbol, the teammates symbol and the right slot. So, this means that you'd need to match two specific symbols in a specific slot for one dot to light up.
Example: 

This symbol I circled in the image above(the symbol the person with the golden code uses) will only fit with this symbol:

in the first slot (space/square) for it to light one of the dots up, but that was in my case, you and your partner will have a different combination.

So, now that you know what you're supposed to do how should you do it then? Well, there's a simple technique @alainmcd posted in one of his treads & this's how to do it: The leader should tell his teammate to fill all their slots with the first symbol in his code (symbol 1 in the next picture) and then tell them (the leader's teammate) to press their button. 
Lets say this is the code with the symbols the leader sent to his teammate:

After the leader's partner fill his slots with his first symbol, it should look like this:
 After filling, remember to press the button!
After that, the leader should put the first symbol in his code in one of the slots and fill the rest with symbols that aren't in his code.
Lets say these are the symbols the leader's teammate sent to the leader:

After the leader has put his first symbol  in one of the slots and filled the rest with symbols he isn't supposed to use/that aren't is his code, it should look like this:
Note: You can see that the symbol that looks like a P with tree legs was in the code in the picture above this one, but the one that look like a R wasn't
then, the leader should press his button to check.
If no dots light up, the leader should put his symbol in the second slot, like this:
And he should press his button again.
If no dots light up again, the leader should put the symbol in the third slot and press his button again...
The leader should keeping repeating it until one of the dots light up or until he has been through every slot with that symbol.
If no dot lit up after the leader has been through every slot with his first symbol, he should change to his second symbol and repeat the same process again.
If one dot light up, you've got a right combination of leader's symbol + teammate's symbol + the correct slot so don't move/change it anymore, keep it like that.
If  that happened, the leader should pay attention to which slot got the match, & not move/change this slot anymore, what he should do now is take out all the wrong symbols( the ones the leader does not have in his code) & tell his partner which slot's the one where there's the right match & then his teammate should take out the symbol in every other slot, but not the one where there's the correct/right match. 
Example:
In this picture you can see that the third slot has a right match, so the partner and the leader should not change it anymore, instead they should take out all the symbols from all other slots.
Then, it should look like this:

After getting your first correct match & taking the rest of the symbols out, the leader should tell to the teammate to fill the rest of their empty slots with their second symbol, and then he should tell to his partner to press their button.
It should look something like this:
Now the leader should fill one slot with his second symbol: & the rest with symbols that he isn't supposed to use:   
Now the leader should press the button to check.
If the second dot didn't light up, the leader should put his second symbol in the next slot & press the button again.
The leader and the partner should keep doing these processes until the six dots light up-
-which then you should follow this guide for solving part 3 of the puzzle. http://forums.kleientertainment.com/topic/77553-metheus-puzzle-part-3-spoilers-updated-with-chest-answers/   Also, there's one last thing I should say's: the Metheus puzzle will probably reset while you're trying to do it, that happens because there's a limited amount of tries you get before the second part of the puzzle resets, but you'll get them right with enough teamwork, eventually. So, don't give up hope & good luck friends !!