The end-Permian extinction, around 252 million years ago, was the biggest die off in Earth's history and removed several whole groups of marine life. The question asks which of the four named fossils belong to groups that never made it past the Permian.
- Favosites: a tabulate coral. The entire tabulate coral group, along with the rugose corals, disappeared completely at the end of the Permian and never reappears in Triassic or younger rocks.
- Phacops: a trilobite. Trilobites as a whole class vanish from the fossil record right at the Permian-Triassic boundary, so any trilobite genus, including Phacops, is extinct by then.
- Aulacopleura: also a trilobite, so the same reasoning applies, its class does not cross into the Mesozoic.
- Lingula: an inarticulate brachiopod that is one of the best known living fossils. It has an almost unbroken record from the early Palaeozoic to today, and living Lingula are still found burrowing in shallow marine mud right now. It was never wiped out.
Three of the four, the coral and the two trilobites, belong to groups the end-Permian extinction removed entirely. The fourth, Lingula, is still alive.
Let's summarize:
- Tabulate corals, such as Favosites, and all trilobites, such as Phacops and Aulacopleura, end at the Permian-Triassic boundary.
- Lingula is a living fossil brachiopod that survives to the present.
So the fossils completely extinct by the end of Permian are Favosites, Phacops, and Aulacopleura.