Final answer:
In dealing with a checked exception, a method in Java must either throw the exception to the caller or catch the exception and handle it within the method.
Step-by-step explanation:
When a method encounters a checked exception in Java, it must handle it in one of two ways: it must either throw the exception to the caller or catch the exception and handle it within the method itself. Throwing an exception requires that the method declares the exception in its signature using the throws keyword, informing the caller of the potential exception. Catching an exception involves the use of a try-catch block where the method attempts to execute code that may cause an exception and provides a mechanism to deal with the exception if it arises.