The correct option is
C Mozart began accompanying his father on tours of the capitals of Europe, to demonstrate his own musical talents
In the original sentence the modifying phrase "At age four" illogically describes "Mozart's father.” To remedy this problem, we need to reword the sentence so that the phrase "At age four” is placed next to "Mozart”, not "Mozart's father.”
Another problem with the original sentence is the word "him”, which is intended to refer to Mozart. The problem is that Mozart only appears as a possessive noun ("Mozart's”), whereas the pronoun "him” is in the objective case. Only a possessive pronoun, such as "his”, can refer back to a possessive noun.
Finally, the pronoun "his" is used ambiguously: does it refer to Mozart or to his father?
(A) This choice is incorrect as it repeats the original sentence.
(B) "Mozart's father" serves illogically as the subject of the opening modifier "starting at age four." Additionally, the pronoun "his" is ambiguous in that it could refer to the boy or the father.
(C) CORRECT. "Mozart" is correctly placed as the subject of the opening modifier "starting at age four." Additionally, the phrase "his own" clarifies that the musical talents in question are those of the subject, Mozart.
(D) The pronoun "his" is ambiguous in that it could refer to Mozart or his father.