Answer
$t=38.1s$
Work Step by Step
The second hand subtends an angle of $2\pi rad$ in $60s$. Its angular speed is $$\omega=\frac{2\pi}{60}=0.105rad/s$$
We have $r=6cm$. In a time t, the second hand moves through an arc $s=24cm$, which corresponds to $$\theta=\frac{s}{r}=4rad$$
The time t it takes is $$t=\frac{\theta}{\omega}=38.1s$$
