The correct options are
C gently
D over his shoulder
The part of a sentence excluding the subject is the predicate. The verb
in the predicate is often modified by an adverb or its equivalent, known
as the adverbial qualification in that predicate.
In the given sentence, "gently" is an adverb of manner and "over his shoulder" is an adverbial phrase that answers the question 'where?'. Hence they both modify the verb "placed" and are the adverbial qualifications. So options C and D are correct. "She" is the subject and "her hand" is the direct object; they do not modify the verb. Hence options A and B are incorrect.