Ta có \(\frac{3 x - 2 y}{4} = \frac{2 z - 4 x}{3} = \frac{4 y - 3 z}{2}\)

\(\Rightarrow \frac{4 \left(\right. 3 x - 2 y \left.\right)}{16} = \frac{3 \left(\right. 2 x - 4 x \left.\right)}{9} = \frac{2 \left(\right. 4 y - 3 z \left.\right)}{4} = \frac{12 x - 8 y - 12 x + 8 y - 6 z}{29}\)

\(\Rightarrow\frac{3 x - 2 y}{4}=0\Rightarrow3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\left(\right.1\left.\right)\)

\(\frac{2 z - 4 x}{3} = 0 \Rightarrow 2 z = 4 x \Rightarrow \frac{x}{2} = \frac{z}{4} \left(\right. 2 \left.\right)\)

Từ (1) và (2) suy ra \(\frac{x}{2} = \frac{y}{3} = \frac{z}{4}\).

Áp dụng ( hoặc theo) tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x + y + z}{2 + 3 + 4}=\frac{18}{9}=2\Rightarrow x=2\cdot2=4;y=2\cdot3=6;z=2\cdot4=8\)