Final answer:
A concave mirror with a focal length of 0.657 m should be used to form the desired image. The mirror should be positioned 0.767 m in front of the object.
Step-by-step explanation:
(a) The type of mirror required to form an image that is six times as tall as the object and positioned 4.6 m from the mirror is a concave mirror. This is because a concave mirror is a converging mirror that can produce magnified, upright images when the object is placed between the focal point and the mirror. In this case, the focal length of the concave mirror is given as 0.657 m.
(b) The mirror should be positioned 0.767 m in front of the object. This distance is less than the focal length of the mirror, which ensures that the image formed is larger and upright.