An electromagnetic wave is transposing energy in the negative y – direction. At one point and one instant the magnetic field is in the positive x – direction. The electric field at that point and instant in:

negative z – direction

In an electromagnetic wave, the direction of energy flow is along the direction of the wave propagation. Therefore, the wave propagates along negative y – direction. Magnetic field ($\vec{B}$) is along the positive x – direction and the wave propagates along negative y – direction. Therefore, electric filed ($\vec{E}$) should be in a direction perpendicular to both x and y - axes. Using vector algebra $\vec{E} × \vec{B}$ should be along negative y – direction.

Since $(-\hat{j})=(-\hat{k}) × (\hat{i}), \vec{E}$ is along negative z - direction.