The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=|-11+6 x| \quad g(x)=\frac{x^{2}+4}{x+4} \quad h(x)=-4+\sqrt{x-5} \] Find \( f\left(\frac{2}{3}\right), g(2) \), and \( h(8) \). Simplify your answers as much as possible. \[ \left(\frac{2}{3}\right)=\square \] \( h(2)=\square \)

First, let's compute \( f\left(\frac{2}{3}\right) \): \[ f\left(\frac{2}{3}\right) = \left| -11 + 6 \cdot \frac{2}{3} \right| = \left| -11 + 4 \right| = \left| -7 \right| = 7 \] Next, we evaluate \( g(2) \): \[ g(2) = \frac{2^2 + 4}{2 + 4} = \frac{4 + 4}{6} = \frac{8}{6} = \frac{4}{3} \] Now, let's find \( h(8) \): \[ h(8) = -4 + \sqrt{8 - 5} = -4 + \sqrt{3} \] So the final answers are: \[ f\left(\frac{2}{3}\right) = 7 \] \[ g(2) = \frac{4}{3} \] \[ h(8) = -4 + \sqrt{3} \]