\begin{equation*}
\begin{split}
\frac{x}{\sin 30^{\text{o}}} &= \frac{4}{\sin 45^{\text{o}}} \\\\
\frac{x}{\frac{1}{2}} &= \frac{4} {\frac{1}{2} \sqrt{2}} \\\\
\frac{x}{\cancel{\frac{1}{2}}} &= \frac{4} {\cancel{\frac{1}{2}} \sqrt{2}} \\\\
\frac {x}{1} & = \frac {4}{\sqrt{2}} \\\\
x & = \frac {4}{\sqrt{2}} {\color {blue} \times \frac {\sqrt{2}}{\sqrt{2}}} \\\\
x & = \frac {4}{2} \sqrt{2} \\\\
x & = 2 \sqrt{2} \text{ cm}
\end{split}
\end{equation*}
