The correct option is C my mother
Some verbs take two objects, a direct object and an indirect object. For
example, in the sentence 'Shaima gave a pen', there is only one object
'pen'. In the sentence 'Shaima gave me a pen', (or 'Shaima gave a pen to
me) there are two objects, 'me' and 'pen', where 'pen' is the direct
object
and 'me' is the indirect object. The indirect object is the recipient of
the direct object.
In the given sentence, the cake is the direct recipient of the verb "baked" and "my mother" is the indirect recipient, as the cake was baked for "my mother", hence option C is correct. As the cake is the direct object, option D is incorrect. "I" is the subject and "baked" is the verb, hence options A and B are incorrect.
Note: The direct object answers the question 'what?'
and the indirect object answers the question 'for whom?'