An electromagnetic wave is represented by the electric field $$\vec{E} = E_0\hat{n}\sin(\omega t + 6y - 8z)$$. Taking unit vectors in x, y and z directions to be $$\hat{i}, \hat{j}, \hat{k}$$, the direction of propagation $$\hat{s}$$, is:

$$\text{The given electric field expression is: } \vec{E} = E_0\hat{n}\sin(\omega t + 6y - 8z)$$

$$\text{Standard form of the wave phase: } \phi = \omega t - \vec{k}_w\cdot\vec{r}$$

$$\text{Comparing the spatial terms: } -\vec{k}_w\cdot\vec{r} = 6y - 8z \implies \vec{k}_w\cdot(x\hat{i}+y\hat{j}+z\hat{k}) = -6y + 8z$$

$$\text{Wave vector: } \vec{k}_w = -6\hat{j} + 8\hat{k}$$

$$\text{Direction of propagation } \hat{s} \text{ is the unit vector along } \vec{k}_w:$$

$$\hat{s} = \frac{\vec{k}_w}{|\vec{k}_w|} = \frac{-6\hat{j} + 8\hat{k}}{\sqrt{(-6)^2 + 8^2}} = \frac{-6\hat{j} + 8\hat{k}}{10} = \frac{-3\hat{j} + 4\hat{k}}{5}$$