An electromagnetic wave is represented by the electric field $\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\hat{\mathrm{n}} \sin \left[\mathrm{\omega t}+\left(6\mathrm{y}-8\mathrm{z}\right)\right]$. Taking unit vectors in $\mathrm{x}, \mathrm{y}$ and $z$ directions to be $\hat{\mathrm{i}}, \hat{\mathrm{j}}, \hat{\mathrm{k}}$ the direction of propagation $\hat{s}$, is:

Given electromagnetic wave is:

$\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\hat{\mathrm{n}} \sin \left[\mathrm{\omega t}+\left(6\mathrm{y}-8\mathrm{z}\right)\right] ....\left(\mathrm{i}\right)$

Comparing it with the standard equation of electromagnetic waves,

i.e., $\mathrm{E}={\mathrm{E}}_0\sin \left(\mathrm{\omega t}-\overrightarrow{\mathrm{k}}.\overrightarrow{\mathrm{r}}\right)$ 

we get, $\overrightarrow{\mathrm{k}}.\overrightarrow{\mathrm{r}}=-\left(6\mathrm{y}-8\mathrm{z}\right)$

or $-\left({\mathrm{k}}_{\mathrm{x}}\hat{\mathrm{i}}+{\mathrm{k}}_{\mathrm{y}}\hat{\mathrm{j}}+{\mathrm{k}}_{\mathrm{z}}\hat{\mathrm{k}}\right).\left(\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{j}}+\mathrm{z}\hat{\mathrm{k}}\right)=6\mathrm{y}-8\mathrm{z}$

$$\begin{gathered} -{\mathrm{k}}_{\mathrm{x}}\mathrm{x}-{\mathrm{k}}_{\mathrm{y}}\mathrm{y}-{\mathrm{k}}_{\mathrm{z}}\mathrm{z}=6\mathrm{y}-8\mathrm{z} \\ \therefore {\mathrm{k}}_{\mathrm{y}}=-6, {\mathrm{k}}_{\mathrm{z}}=8, {\mathrm{k}}_{\mathrm{x}}=0 \end{gathered}$$

Hence, $\hat{\mathrm{s}}=\frac{-6\hat{\mathrm{j}}+8\hat{\mathrm{k}}}{10}=\frac{-3}{5}\hat{\mathrm{j}}+\frac{4}{5}\hat{\mathrm{k}}$