From the image, this organism has lacy feeding structures which are most likely lophophores, meaning that it is probably a Lophotrochozoan. Since it also has deuterostome development, it must be from one of the phyla which has this kind of development, such as the Annelida. It must be a Bilaterian since it is a Lophotrochozoan, and that also makes it a Metazoan and a Eumetazoan.
Work Step by Step
Skim the chapter and use the key hint that this organism has a lophophore but also deuterostome-type development. This will lead to a few possible phyla, which then, by implication, shows which major clades are involved.