Burn the Summer Palace is a decision available to any great power, who are at war with 
China.
It shows up in the decision tab if a great power is at war with China, has researched Nationalism and Imperialism and China owns Beijing (province no 1612).
It is possible to take if the great power has occupied Beijing.
It gives 3 infamy and gives China the event Torching of the Summer Palace, which gives China 5 war exhaustion and removes 25 prestige from China.
It is from a purely strategic viewpoint not worth to take, as it does not do any thing positive for the nation, other than giving China war exhaustion, which makes it easier to win the war. If the Great power is in a position, where it has occupied Beijing, the war should be winable anyway.