The correct option is
C Who
The given sentence is a complex sentence which is made up of two sentences. 'The woman gave me the money'. 'The woman was quite young'. The two sentences have been combined using a relative pronoun, that works as a conjunction. All the options given are relative pronouns that work as conjunctions. The relative pronouns have different forms as under:
Who: Nominative case i.e. It refers to the Subject/doer of the action. It always refers to a person/ persons.
Whom: Accusative/ objective case. It refers to the object/ receiver of the action word.
Whose: Genitive/ possessive case i.e show ownership/ possession.
Which: Used to refer to a non-living thing or animal or an idea.
In the given sentence, the pronoun qualifies the subject- 'woman', which is a common that refers to a person and not to a non-living thing. The woman is the doer of the action ('gave me money'/'is young' etc) and is in Nominative case. Hence, option A is incorrect.
Option B is incorrect as there is no reference to ownership of anything/relationship between any two nouns in the given sentence.
Option C: As the subject, 'woman' is a person and is in the nominative case, 'who' is the most appropriate relative pronoun to be used.
Option D: In the given sentence, 'woman' is the subject, and not the object. Hence, this is incorrect.