The fence was very strong. in this sentence is a predicate .

The predicate is the very and everything that follows after it, which could include adverbs, prepositional phrases, and other parts of speech.  For example, "The dog ran across the street to the neighbor's house".  Find the verb (the action or in your case, a linking verb such as is, are, was, wear, am).  In my example, the verb is 'ran'.  So the predicate is:

    -ran across the street to the neighbor's house

For your sentence, the predicate is -was very strong.