E and H relationship
I guess you have an error in your calculation of the cross product. As you don't show your calculation, I can't tell what the error is, but I guess you forgot that the second row of the result differs a bit from the others...

Here is my step-by-step calculation. Sorry for the slightly different notation...

$$\vec{H}=-100\cdot\begin{pmatrix}1\\0\\0\end{pmatrix}\times\begin{pmatrix}0\\10\\20\end{pmatrix}\cdot e^{-j4x}\cdot10^{-3}$$

$$=-100\cdot\begin{pmatrix}0\cdot20-0\cdot10\\ 0\cdot0-1\cdot20\\1\cdot10-0\cdot0\end{pmatrix}\cdot e^{-j4x}\cdot10^{-3}$$

$$=-100\cdot\begin{pmatrix}0\\ -20\\+10\end{pmatrix}\cdot e^{-j4x}\cdot10^{-3}$$

$$=\begin{pmatrix}0\\ +2\\-1\end{pmatrix}\cdot e^{-j4x}$$

$$=(-\vec{e}_z+2\vec{e}_y)\cdot e^{-j4x}$$