\(\frac{x}{2}=\frac{2y}{3}=\frac{3z}{4}=>\frac{x}{2}.\frac{2y}{3}.\frac{3z}{4}=\frac{x}{2}.\frac{x}{2}.\frac{x}{2}\)
=>\(\frac{x.2y.3z}{2.3.4}=\frac{x^3}{2.2.2}\)
=>\(\frac{xyz.6}{24}=\frac{x^3}{8}\)
=>\(\frac{x^3}{8}=\frac{108.6}{24}\)
=>\(\frac{x^3}{8}=27\)
=>\(x^3=27.8=>x^3=216=6^3=>x=6\)