Here's why:
* Predicate Adjective: A predicate adjective modifies (describes) the subject of the sentence and follows a linking verb.
* Subject: The subject is "John's life".
* Linking Verb: The linking verb is "was".
* Predicate Adjective: The word "difficult" describes the subject "John's life".
The second sentence "He worked hard at home" is a separate sentence and does not have a predicate adjective within it.