Although both front and rear doors were found open after the burglary, there were pry marks around the lock on the rear door and deposits of mud near the threshold. It must be the case that the thief entered through the rear door and left through the front.

inductive; causal inference

Explanation:

This is inductive because a broad generalization (that the thief entered through the rear door and left through the front) came from specific observation (both doors were found open but pry marks and mud were found around the rear door) gave the conclusion that they entered through the rear and left through the front. in other words what was observed around the rear door brought about that conclusion.

In a causal inference, somebody tries to come to the conclusion that something is, or could be, the cause of something else.