A box of mass 15 kg is kept on the floor of a stationary trolley....

Let the acceleration of the trolley be $a$.

In the frame of the trolley, a pseudo force $ma$ acts on the box in the direction opposite to the motion.

For the box to remain stationary relative to the trolley, the static friction force must balance this pseudo force.

The maximum static friction force available is given by $f_{s,\text{max}} = \mu_s N = \mu_s mg$.

Equating the pseudo force to the maximum static friction force gives the maximum acceleration:

$ma_{\text{max}} = \mu_s mg$

$a_{\text{max}} = \mu_s g$

Substituting the given values $\mu_s = 0.12$ and $g = 10$ m/s$^2$:

$a_{\text{max}} = 0.12 \times 10 = 1.2$ m/s$^2$

Answer: $1.2$