Basis of classification

Triploblastic animals have three embryonic germ layers: ectoderm, mesoderm and endoderm.
Platyhelminthes (flat worms) to chordates are triploblastic; flat worms are triploblastic, acoelomate and bilaterally symmetrical.
Corals (coelenterates) and ctenophores are diploblastic, with only ectoderm and endoderm separated by mesoglea.
Sponges have a cellular level of organisation without true germ layers or tissues.
Hence flat worms are triploblastic.

In round worms (Aschelminthes) the body cavity is not lined by mesoderm; the mesoderm is present as scattered pouches between the ectoderm and endoderm. Such a cavity is a pseudocoelom, so round worms are pseudocoelomates. This statement is correct.
Flat worms (Platyhelminthes) have no body cavity at all; they are acoelomates.
Molluscs have a true coelom lined by mesoderm; they are coelomates.
Insects (arthropods) are also true coelomates.
Hence the correct statement is that round worms are pseudocoelomates.

Sponges are mostly asymmetrical and have a cellular level of organisation without true germ layers.
Coelenterates and ctenophores are radially symmetrical and diploblastic (two germ layers, ectoderm and endoderm).
Aschelminthes (round worms) are bilaterally symmetrical, triploblastic and pseudocoelomate animals with an organ-system level of organisation.
Hence the group that is bilaterally symmetrical and triploblastic is Aschelminthes.