\begin{equation*}
\begin{split}
\frac{x}{\sin 30} &= \frac{4}{\sin 45} \\\\
\frac{x}{\frac{1}{2}} &= \frac{4} {\frac{1}{2} \sqrt{2}} \\\\
x & = \frac{4} {\frac{1}{2} \sqrt{2}} \times \frac 12 \\\\
x & = \frac{4} {\sqrt{2}} {\color {blue} \times \frac {\sqrt{2}}{\sqrt{2}}} \\\\
x & = 2 \sqrt{2}
\end{split}
\end{equation*}