To solve the button puzzle in Kadish Tolesa, recall the spinning prisms in the puzzle room:
The pillars show from left to right, the D'ni numbers 1 to 6.
Now examine the icons on the buttons panel:
If you look at the 4 icons associated with each button you will see that they match those in the puzzle room. For each button work out which icons are present and list the numbers that match those icons. For example, button 1 shows the icons for 2, 3, 4 and 6.
The results are (ignoring the duplicates):
Button 1: 2 3 4 6
Button 2: 4 5 6
Button 3: 2 5 6
Button 4: 21 2 3 6
Button 5: 1 3 4 5
Button 6: 2 3 4 5
Now work out which ones are missing:
Button 1: 1 5
Button 2: 1 2 3
Button 3: 1 3 4
Button 4: 4 5
Button 5: 2 6
Button 6: 1 6
You can see from the panel that you have to press button 1 first so eliminate all the 1s from the missing list. You can also eliminate the 5 from button 1 since we already know that this is the first button:
Button 1: first
Button 2: 2 3
Button 3: 3 4
Button 4: 4 5
Button 5: 2 6
Button 6: 6
You can now see that Button 6 will be the sixth button to press so eliminate the sixes:
Button 1: first
Button 2: 2 3
Button 3: 3 4
Button 4: 4 5
Button 5: 2
Button 6: sixth
Button 5 is the second button to press so remove all the twos:
Button 1: first
Button 2: 3
Button 3: 3 4
Button 4: 4 5
Button 5: second
Button 6: sixth
Button 2 is the third button to press so remove all the threes:
Button 1: first
Button 2: third
Button 3: 4
Button 4: 4 5
Button 5: second
Button 6: sixth
Button 3 is the fourth button to press so remove all the fours:
Button 1: first
Button 2: third
Button 3: fourth
Button 4: 5
Button 5: second
Button 6: sixth
Leaving us with button 4 which is the fifth button to press.
Press the buttons in the order: 1 5 2 3 4 6.
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