What kind of fault results in the right side falling and the left side rising?

The correct understanding here is that a reverse fault occurs when the earth's crust is subjected to compressive forces. In this type of faulting, the hanging wall moves upwards relative to the footwall. In the context of your question, when the right side of a fault falls while the left side rises, it indicates that the hanging wall on the right side has moved upward due to the compression, which is characteristic of a reverse fault. This upward movement on one side and downward movement on the other side illustrates the mechanics of how stress within the Earth's crust can create distinct geologic features and result in the formation of mountains and other landforms.

Normal faults, on the other hand, occur when the crust is under tension, resulting in the hanging wall moving downwards. Strike-slip faults involve horizontal movement where blocks slide past each other rather than moving up or down, and transform faults specifically refer to lateral movement, where two tectonic plates slide past each other while remaining at roughly the same elevation. Understanding the mechanics of these various types of faults helps to clarify why a reverse fault is correctly identified in this scenario.