$$\large\textbf{Step 1:Calculate position of the Image}$$
Given,
As object is placed in front of mirror (to the left of the mirror), the object distance is negative
Object distance, $$u = -12 cm$$
Convex mirror focal length, $$f = +30 cm$$ (as the mirror is convex)
Height of the candle $$h_o = 2.5 cm$$
We know,
By Mirror formula
$$\frac{1}{f} $$ $$=$$$$\frac{1}{v} $$ + $$\frac{1}{u} $$
Or $$\frac{1}{v} $$ $$=$$ $$\frac{1}{+30} $$ $$-$$ $$\frac{1}{-12} $$
Or $$v = +8.571 cm$$
Image formed behind the mirror at distance $$= +8.571 cm$$
$$\large\textbf{Step 2: Calculate Magnification }$$
We know,
magnification of image, $$m=\frac{-v}{u}$$
Therefore,
$$m=-\frac{+8.571}{-12} = +0.741$$
Height of the Image is given by the $$ h_i = m h_o$$
$$ h_i = {0.741}\times 2.5 = 1.78 cm$$