Answer
$50\;\rm cm$
Work Step by Step
We know that the distance between the two lenses is 30 cm and the right lens has a 20 cm focal distance while the left one has a 15 cm focal distance. See the figure below.
The final image which is the image of the right lens is in the middle between the two lenses. Thus, $d_{i,\rm right}=15\rm\;cm$.
Now we need to find the image of the left lens which is the object of the right lens.
$$\dfrac{1}{f_{\rm right}}=\dfrac{1}{d_{o,\rm right}}+\dfrac{1}{d_{i,\rm right}}$$
Solving for $d_{o,\rm right}$;
$$\dfrac{1}{f_{\rm right}}-\dfrac{1}{d_{i,\rm right}}=\dfrac{1}{d_{o,\rm right}}$$
$$d_{o,\rm right}=\left[\dfrac{1}{f_{\rm right}}-\dfrac{1}{d_{i,\rm right}}\right]^{-1}$$
Plugging the known;
$$d_{o,\rm right}=\left[\dfrac{1}{ 20}-\dfrac{1}{-15}\right]^{-1}=\bf 8.57 \;\rm cm$$
This means that the image of the left lens is given by
$$d_{i,\rm left}=30-8.57 =\bf 21.43\;\rm cm$$
Now we have the focal length of the left lens, and the image distance of it, and we just need to find the object distance.
$$\dfrac{1}{f_{\rm left}}=\dfrac{1}{d_{o,\rm left}}+\dfrac{1}{d_{i,\rm left}}$$
Solving for $d_{o,\rm left}$;
$$\dfrac{1}{f_{\rm left}}-\dfrac{1}{d_{i,\rm left}}=\dfrac{1}{d_{o,\rm left}} $$
$$\dfrac{1}{f_{\rm left}}-\dfrac{1}{d_{i,\rm left}}=\dfrac{1}{d_{o,\rm left}} $$
$$d_{o,\rm left} =\left[\dfrac{1}{f_{\rm left}}-\dfrac{1}{d_{i,\rm left}}\right]^{-1} $$
Plugging the known;
$$d_{o,\rm left} =\left[\dfrac{1}{15}-\dfrac{1}{21.43}\right]^{-1} =\color{red}{\bf 50}\;\rm cm $$
