Question

Select the abbreviation that tells how the italicized noun clause is used.

S-subject, DO-direct object, SC-subject complement, OP-object of preposition
I am optimistic enough to believe that young people will respond to a challenge.
S
OP
SC
DO

Answer 1

Since the noun clause in this example is '(that) young people will respond to a challenge', the correct answer is DO, it is a direct object. Because believe is a transitive verb, and requires a direct object. 

Answer 2

The abbreviation that tells how the italicized noun clause is used is DO. The fourth option is correct.

The clause: "that young people will respond to a challenge" is a direct object. This clause cames right after the verb believe which is a transitive verb which requires a direct object to conve a compkete thought that makes sense.

The direc object is a noun phrase denoting a person or thing that is the recipient of the action of a transitive verb