A small electric dipole is placed at origin with its dipole moment directed along positive x -axis. The direction of electric field at point $\left(2,2\sqrt{2},0\right)$is:

The electric field due to a dipole at any point in space is given by,
$E=1/(4\pi {ϵ}_0{r}^3)(3(\overrightarrow{p}.\hat{r})\hat{r}-\overrightarrow{p})$

$r=2\hat{i}+2\sqrt{2}\hat{j}\Rightarrow \hat{r}=1/\sqrt{3}\hat{i}+\sqrt{\frac{2}{3}}\hat{j}$

$E=1/(4\pi {ϵ}_0{r}^3)(\sqrt{3}p\hat{r}-p\hat{i})$
The i component cancels out leaving only the j component.