Find the shortest distance between the following two lines \({g}_{1}\) and \({g}_{2}:\)
\[ \begin{align}
{g}_{1} &: \frac{x-3}{2} = \frac{y+1}{-2} = z-2 \\
{g}_{2} &: x = \frac{y}{2} = -z+4.
\end{align}\]

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