The object distance for a convex lens is 20.0 cm and the image distance is 4.0 cm. the height of the object is 10.0 cm. what is the height of the image? 50.0 cm 8.0 cm 2.0 cm 0.50 cm

We can use the magnification formula to calculate the height of the image: 

Hi/H0=-(Di/D0), where Hi is height of the image, H0 is height of the object, Di is the distance of the image and D0 is the distance of the object. 
We need to solve for Hi:

H0=10.0 cm
Di=4.0 cm
D0=20.0 cm
Hi=?

Hi/H0=-(Di/D0), we multiply by H0,

Hi=-(Di/D0)*H0=-(4/20)*10=-2.0 cm

The height of the image is Hi=2.0 cm so the correct answer is the third option: 2.0 cm. The minus sign tells us the image is inverted.