In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $z$-axis and magnetic field is along the positive $x$-axis. Then the direction of propagation of electromagnetic wave is:

As the electric field is along the negative $z$-axis and the magnetic field is along the positive $x$-axis, the direction of propagation of the wave is given by the vector product $\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}}$, which is in the direction of the negative $y$-axis. <br/><br/> Using the right-hand rule, if you point your right thumb in the direction of the vector product $\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}}$, your fingers will curl in the direction of the propagation of the wave. In this case, the fingers would curl in the direction of the negative $y$-axis. <br/><br/> Therefore, the direction of propagation of the electromagnetic wave in this scenario is along the negative $y$-axis.