\[\begin{align}  & \underset{x\to 2}{\mathop{\lim }}\,\frac{2-\sqrt[3]{3x+2}}{5{{x}^{2}}-18x+16}=\underset{x\to 2}{\mathop{\lim }}\,\frac{(2-\sqrt[3]{3x+2})\times \left( 4+2\sqrt[3]{3x+2}+\sqrt[3]{{{\left( 3x+2 \right)}^{2}}} \right)}{\left( x-2 \right)\left( 5x-8 \right)\times \left( 4+2\sqrt[3]{3x+2}+\sqrt[3]{{{\left( 3x+2 \right)}^{2}}} \right)}=\underset{x\to 2}{\mathop{\lim }}\,\frac{-3\left( x-2 \right)}{\left( x-2 \right)\left( 5x-8 \right)\times \left( 4+2\sqrt[3]{3x+2}+\sqrt[3]{{{\left( 3x+2 \right)}^{2}}} \right)}= \\  & \frac{-3}{\left( 5\times 2-8 \right)\times \left( 4+2\sqrt[3]{3\times 2+2}+\sqrt[3]{{{\left( 3\times 2+2 \right)}^{2}}} \right)}=\frac{-3}{2\times \left( 4+4+4 \right)}=-\frac{1}{8} \\ \end{align}\]