***** NOT A TEACHER *****
(1) I believe that the correct answer is A.
(a) What did Tom suggest?
(i) Answer: buying a new car.
(b) Whose buying a new car? My buying a new car.
In other words: Tom suggested that I buy a new car.
(Many native speakers say: Tom suggested me buying a new car.)
(2) With the greatest respect, I do not believe many native speakers would
say (b). You could say:
Tom advised/told/ ordered/allowed me to buy a new car.
(Be careful about what you read on the Web -- including this post of
Student or Learner