\(\frac{x}{20}=\frac{y}{9}=\frac{z}{6}\Leftrightarrow\frac{x}{20}=\frac{2y}{18}=\frac{4z}{24}=\frac{x-2y+4z}{20-18+24}=\frac{13}{26}=\frac{1}{2}\)
\(\Rightarrow x=\frac{1}{2}.20=10\)
\(\Rightarrow y=\frac{\frac{1}{2}.18}{2}=\frac{9}{2}\)
\(\Rightarrow z=\frac{\frac{1}{2}.24}{4}=3\)