\(2x:6=5:3\) \(-\frac{2}{x}=-\frac{x}{8}\)
\(\Rightarrow2x:6=\frac{5}{3}\) \(\Rightarrow-2\times8=x\times\left(-x\right)\)
\(\Rightarrow2x=\frac{5}{3}\times6\) \(\Rightarrow-16=\left(-x\right)^2\)
\(\Rightarrow2x=10\) \(\Rightarrow\left(-4\right)^2=\left(-x\right)^2\)
\(\Rightarrow x=5\) \(\Rightarrow x=-4\)