Step 1: Understanding the Events.
- P: Earliest evidence of terrestrial arthropods dates back to the Silurian period, about 430 million years ago.
- Q: The appearance of Ediacaran fauna occurred around 635 million years ago, prior to the Cambrian explosion.
- S: Mammals originated around 300 million years ago during the late Carboniferous period.
- R: The extinction of large non-flying dinosaurs happened about 65 million years ago at the end of the Cretaceous period.
Step 2: Conclusion.
Thus, the correct chronological order is (D): Q, P, S, R.