If $f(x)=\dfrac{4x+3}{6x-4}$, $x\ne\dfrac{2}{3}$, and $(f\circ f)(x)=g(x)$, where $g:\mathbb{R}-\left\{\dfrac{2}{3}\right\}\to\mathbb{R}-\left\{\dfrac{2}{3}\right\}$, then $(g\circ g\circ g)(4)$ is equal to: