When a person exhibits success facing everyday, real-world demands such as those found in on-the-job professional demands, Sternberg's triarchic theory of intelligence would suggest that person was demonstrating:

contextual intelligence.

Explanation:

Contextual intelligence: In psychology, the term "contextual intelligence" is described as an individual's capabilities to apply his or her practical knowledge to the real world situations and scenarios. It refers to the proficiency of an individual to adapt skills and knowledge to a variety of environment or situations. Along with this he or she modify situations to accomplish a specific goal.

In the question above, "Sternberg's triarchic theory of intelligence would suggest that person was demonstrating contextual knowledge".