The opposite hexagram is formed by changing all six lines of a hexagram into their opposites: every yin line turns yang and every yang line turns yin. The trigrams flip too: Heaven becomes Earth, Water becomes Fire, Thunder becomes Wind, Mountain becomes Lake.
Names
It's known as 錯卦 (cuòguà), a term made popular by the Ming dynasty scholar Lai Zhide. Long before, in the Han dynasty, Yu Fan used 旁通, "side-by-side connection," for the same relationship. In English you'll also see "complementary hexagram."
Examples
- Activity and Passivity: all yang against all yin.
- Water and The Flame.
- Initial Obstacles has The Vessel of Nourishment as its opposite.
What it shows you
The opposite is the other side of your situation: what's missing, what's in shadow, or the attitude contrary to the one the moment asks for. Some readers look at it to see what they're overlooking.
It isn't the same as the inverted hexagram, which turns the figure upside down without changing any line. Nor is it the relating hexagram, although the two match in one case: when all six lines of your cast are moving.
In the King Wen sequence, the eight hexagrams that look the same upside down are paired with their opposites. Like the nuclear hexagram, it's a tool for going deeper, not a required step.