Answer
36.0 cm.
Work Step by Step
Use the mirror equation.
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{f}$$
For a real image, $s’ \gt 0$, so $m=-\frac{s’}{s}$ is negative. The image height is the same as the object height, so s’=s.
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{s}+\frac{1}{s}=\frac{2}{s}$$
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{f}=\frac{1}{18.0 cm}$$
Comparing the right hand sides, we see that s = 36.0 cm.
