This is a special character of coelenterata occurring only in them

The correct option is Nematocysts.

Let us break down the explanation step-by-step to understand why this is the correct answer:

1. Understanding Nematocysts: Nematocysts (also known as cnidae) are specialized, stinging organelles found inside cells called cnidocytes or nematocytes. These organelles contain a coiled, hollow thread that can be rapidly discharged to inject toxins into prey or predators. They are primarily used for defense, food capture, and attachment.

2. Exclusivity to Coelenterata (Cnidaria): Nematocysts are the defining characteristic of the phylum Coelenterata (which is also called Cnidaria, named precisely after these cnidocytes). They do not naturally develop or occur in any other animal phylum. Any occurrence in other organisms (like certain nudibranch mollusks) is due to ingestion and hijacking of the coelenterate's nematocysts, rather than native production.

3. Analyzing the Other Options:
• Flame cells: These are specialized excretory and osmoregulatory cells found in Platyhelminthes (flatworms), not coelenterates.
• Hermaphroditism: This is a reproductive state where an organism has both male and female reproductive organs. It is common across many different phyla (such as Platyhelminthes, Annelida, and Mollusca) and is not exclusive to Coelenterata.
• Polymorphism: This refers to the occurrence of more than one distinct form (like polyp and medusa) in the life cycle of an organism. While highly pronounced in coelenterates, polymorphism also occurs in other animal groups (e.g., social insects like ants and bees) and is therefore not unique to coelenterates.

Thus, nematocysts are the only special character listed that occurs exclusively in the phylum Coelenterata.