Given:
Focal length \( f = 18 \, {cm} \)
Magnification \( M = -2 \)
We use the mirror formula:
\[
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
\]
where:
\( v \) is the image distance,
\( u \) is the object distance.
Also, magnification \( M \) is given by:
\[
M = \frac{v}{u}
\]
Substitute \( M = -2 \):
\[
-2 = \frac{v}{u} \quad \Rightarrow \quad v = -2u
\]
Now substitute \( v = -2u \) into the mirror equation:
\[
\frac{1}{18} = \frac{1}{-2u} + \frac{1}{u}
\]
Simplify the equation:
\[
\frac{1}{18} = \frac{-1 + 2}{u} \quad \Rightarrow \quad \frac{1}{18} = \frac{1}{u}
\]
Thus,
\[
u = 18 \, {cm}
\]
So, the object should be placed 18 cm in front of the mirror to obtain the desired image.