Equation of a one dimensional transverse progressive wave is given by  $s=6\sin (5t-3x+4y-12z+\frac{\pi }{6})$Here, s is displacement of medium at time t as a function of coordinates x,y and z in m. Wavelength (in m) of the wave is 
 

Equation of displacement of progressive wave is of the form
   $s=A\sin (\omega t-k\cdot r+\varphi )$
 On comparison with given wave equation, we get 
   $$\begin{gathered} k\cdot r=-3x+4y-12z \\ \Rightarrow k\cdot (x\widehat{i}+y\widehat{j}+z\widehat{k})=-3x+4y-12z \\ \Rightarrow k=-3\widehat{i}+4\widehat{j}-12\widehat{k} \\ \Rightarrow k=\left|k\right|=\sqrt{3^2+4^2+{12}^2}=13 \\ \Rightarrow \frac{2\pi }{\lambda }=13 \\ \Rightarrow \lambda =\frac{2\pi }{13} \end{gathered}$$