In the diagram below, we have $XY = 2\cdot AX = 2\cdot YB$ and $\dfrac{AZ}{ZC} = \dfrac{2}{3}$. Find $\dfrac{[YBC]}{[ZYC]}$. [asy] pair A, X, Y, B, Z, C; A = (0,0); X = (0.3,-0.2); Z = (0.4,0.2); Y = 3*X; B = 4*X; C = 2.5*Z; draw(X--Z--Y--C--B--A--C); label("$A$",A,W); label("$B$",B,S); label("$C$",C,N); label("$X$",X,SW); label("$Y$",Y,SW); label("$Z$",Z,NW); [/asy]
