The predicate is the part of a sentence (or clause) that contains a verb, stating what the subject is doing, or describes the subject.
When we have a main verb and an auxiliary verb accompanying it, both of them together form the predicate. In the given sentence, we have a construction with a main verb<em> to study </em>and an auxiliary verb <em>should:</em> <em>should be studying</em>. If you chose just<em> studying</em> or <em>should be</em> as the predicate, that would be incorrect as those two options are not the complete predicate.
