A plane glass mirror of thickness 3 cm of material of $\mu = \frac{3}{2}$ is silvered on the back surface. When a point object is placed 9 cm from the front surface of the mirror, then the position of the brightest image from the front surface is

The brightest image is formed by light that refracts into the glass, reflects from the silvered back surface, and refracts back out.

Refraction at front surface: Apparent distance of object from front surface as seen inside glass:
$u' = \mu \times u = \dfrac{3}{2} \times 9 = 13.5$ cm

Reflection at silvered back surface: Distance of apparent object from back mirror $= 13.5 + 3 = 16.5$ cm

Plane mirror forms image 16.5 cm behind the back surface. Distance of this image from the front surface (inside glass) $= 16.5 + 3 = 19.5$ cm

Refraction back out at front surface: Final apparent distance from front surface as seen in air:
$v' = \dfrac{v}{\mu} = \dfrac{19.5}{\dfrac{3}{2}} = 19.5 \times \dfrac{2}{3} = 13$ cm