$\therefore $ Time period, $\mathrm{T}=8$ $sec.$

$\lambda=24 \mathrm{\,m}$

$\mathrm{v}=\mathrm{f} \lambda$

$=3 \mathrm{\,m} / \mathrm{s} \ldots \ldots \ldots(1)$

Time taken by particle to travel $9 \mathrm{\,m}$ is

$=\frac{9}{3}=3 \mathrm{\,sec}$

Now, time taken by particle to reach lower extreme first time

is $\frac{3 T}{4}=\frac{3}{4} \times 8$

$=6$ $sec.$ $\ldots \ldots(2)$

$\therefore $ Total time taken $=3 \mathrm{\,sec}+6 \mathrm{\,sec}$

$=9$ $sec$