Which of the following is not a possible de-Broglie's wavelength of a particle, which moves inside a cubical box of side length L, without losing any energy (elastically colliding with walls of cube)?

Using concept of stationary waves, we can say at rigid walls Node formation takes place.

$L=\frac{\lambda }{2}, \lambda , \frac{3\lambda }{2}, 2\lambda ..., \frac{n\lambda }{2} where n=1,2,3...$ 

Longest wavelength is specified by $\lambda =2L.\text{ next by }\lambda =L$
then $\lambda =L\times \frac{2}{3}.\text{ etc }$
$\text{ In general }{\lambda }_n=\frac{2L}{n},n=1,2,3,\dots$
For(a) $\lambda =\frac{2L}{3}$
For (b) $\lambda =L$
For (c) )$\lambda =2L\text{ . }$Hence, all are possible.