Let's say you're trying to figure out whether you left your coat at work. You could drive to the office and look for it there, and that will definitely tell you the answer. But if you look in your closet at home, then you know that the coat is definitely not at work, so you're done.
If you don't find the coat in your closet, you will don't know whether you left it at work. It could be in your car or maybe you left it on the train. But it's still worth checking your closet first because that gives you an early possible solution.
In logic, that's: If coat is at work, then closet is empty.
X = "Coat is at work".
Y = "Closet is empty".
Modus tollens tells us that "If X, then Y" implies "If not Y, then not X." So: If closet is not empty, then coat is not at work.
If you don't find the coat in your closet, you will don't know whether you left it at work. It could be in your car or maybe you left it on the train. But it's still worth checking your closet first because that gives you an early possible solution.
In logic, that's: If coat is at work, then closet is empty.
X = "Coat is at work".
Y = "Closet is empty".
Modus tollens tells us that "If X, then Y" implies "If not Y, then not X." So: If closet is not empty, then coat is not at work.