magnification of an image formed by a lens is given by the ratio of the height of the image to the height of the object. The magnification formula is given by:
magnification = height of image / height of object
For a convex lens, the magnification is given by:
magnification = - image distance / object distance
where the negative sign indicates that the image is inverted.
In this case, the object distance is 6.0 cm and the focal length is 9.0 cm. Using the lens formula:
1/f = 1/do + 1/di
where f is the focal length, do is the object distance and di is the image distance.
Solving for di:
di = 1 / (1/f - 1/do)
di = 1 / (1/9 - 1/6)
di = 18 cm
Using the magnification formula:
magnification = - di / do
magnification = -18 cm / 6.0 cm
magnification = -3.0