How the rule works
Every cell has three slots in a row with one symbol each, or empty. The third cell is worked out slot by slot from the first two: one symbol is neutral and changes nothing, two equal symbols become the neutral one, and two different symbols among the other three become the third. The answer says which symbol is neutral and which the other three are. The rule holds in rows and columns at the same time.
This is the rule that makes the harder tests hard: the table cannot be guessed, it has to be read from the complete rows. Look for a row where two equal symbols stand in the same slot in the first two cells, and see what stands there in the third. That is the neutral symbol. The rest follows.