The correct answer is option 3, Sunderbans. The Sunderbans is the largest existing mangrove forest in the world. It is located in the delta region of the Ganges, Brahmaputra, and Meghna rivers in India and Bangladesh.
Option 1, African forest is incorrect as there is no specific mangrove forest in Africa comparable in size to the Sunderbans.
Option 2, Alpine forest is incorrect as this refers to forests found in mountainous regions, which are distinct from mangrove forests which grow in coastal regions.
Option 4, Australian forest is incorrect as while Australia is home to several significant mangrove forests, none of them are larger than the Sunderbans.
Therefore, the largest existing mangrove forest in the world is the Sunderbans.