Step 1: Break down the clue.
The animal is triploblastic, meaning it has three germ layers. But it has no body cavity. We must find which given animal fits both clues.
Step 2: Define an acoelomate.
An animal with three germ layers but no coelom is called an acoelomate. Flatworms are the classic acoelomates.
Step 3: Check Ascaris.
Ascaris is a roundworm. It has a false body cavity called a pseudocoelom, so it does have a cavity. It does not fit.
Step 4: Check Pheretima and Asterias.
Pheretima (earthworm) and Asterias (starfish) both have a true coelom, so they are eucoelomates. Neither fits the "no body cavity" clue.
Step 5: Check Fasciola.
Fasciola is the liver fluke, a flatworm. It is triploblastic and has no body cavity, so it is an acoelomate. This matches both clues perfectly.
Step 6: State the answer.
The triploblastic animal without a body cavity is Fasciola.
\[ \boxed{\text{Fasciola}} \]