AMO · 2027 · Grades 8-9 · Self-study SET 24 Question 11

For positive real numbers $x,y,z$,
$$\frac{x}{3y+2z}+\frac{3y}{x+2z}+\frac{2z}{x+3y}=\frac32.$$
Find $\dfrac{(7x+12y)^2}{z^2}$. Enter the number.