(a) -15.2 cm
We can solve the problem by using the lens equation:

where
f = -22.8 cm is the focal length of the lens (negative because it is a diverging lens)
p = 45.6 cm is the distance of the object from the lens
q is the distance of the image from the lens
Solving the equation for q, we find the position of the image:


and the negative sign means that the image is virtual.
(b) -11.4 cm
In this case, the distance of the object from the lens is
p = 22.8 cm
Substituting into the lens equation, we can find the new image distance, q:


and the negative sign means that the image is virtual.
(c) -7.6 cm
In this case, the distance of the object from the lens is
p = 11.4 cm
Substituting into the lens equation, we can find the new image distance, q:


and again, the negative sign means that the image is virtual.