Answer
12.0 cm.
Work Step by Step
Use the mirror equation.
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{f}$$
For a convex mirror, the image is virtual, $s’ \lt 0$, so $m=-\frac{s’}{s}$ is positive. The image height is half the object height, so m = 0.5 and s’=-s/2.
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{s}-\frac{2}{s}=-\frac{1}{s}$$
$$\frac{1}{s}+\frac{1}{s’}=\frac{1}{f}=\frac{1}{-12.0 cm}$$
Comparing the right hand sides, we see that s = 12.0 cm.
