Reptiles, such as the thrny devl and Gila mnster, can be found in the middle of deserts, whereas most amphibians do not stray too far from water. Which adaptation allows for this increased range of reptiles?

The adaptation is most likely the fact that reptiles can lay eggs on land. Amphibians can only lay eggs in the water, which means in order to reproduce they must be near a safe body. Reptile eggs contain water inside of them, so the eggs can hatch on the land instead of developing in the water.