Final answer:
The red-eared slider is part of the Reptilia class and the order Testudines, specifically within the suborder Cryptodira.
Step-by-step explanation:
The taxonomy of a red-eared slider, which is a type of turtle, can be understood by looking at its position within the order Testudines. Testudines is part of the class Reptilia and encompasses all turtles, including the red-eared slider. This order is then further divided into two suborders: Cryptodira and Pleurodira. Red-eared sliders belong to the suborder Cryptodira, which are turtles that can draw their necks inside their shell in a vertical S-curve. All turtles in the order Testudines share common traits like a bony or cartilaginous shell made up of the carapace and the plastron, and they all lay eggs on land, having evolved around 200 million years ago.