\(3\sqrt{48}-14\sqrt{\dfrac{1}{3}}-\dfrac{4}{2+\sqrt{3}}\)
\(=3\cdot4\sqrt{3}-14\cdot\dfrac{\sqrt{1}}{\sqrt{3}}-\dfrac{4\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\)
\(=12\sqrt{3}-\dfrac{14}{\sqrt{3}}-\dfrac{4\left(2-\sqrt{3}\right)}{2^2-\left(\sqrt{3}\right)^2}\)
\(=12\sqrt{3}-\dfrac{14}{\sqrt{3}}-\dfrac{4\left(2-\sqrt{3}\right)}{1}\)
\(=12\sqrt{3}-\dfrac{14}{\sqrt{3}}-4\left(2-\sqrt{3}\right)\)
\(=12\sqrt{3}-\dfrac{14}{\sqrt{3}}-8+4\sqrt{3}\)
\(=16\sqrt{3}-\dfrac{14}{\sqrt{3}}-8\)
\(=\dfrac{48}{\sqrt{3}}-\dfrac{14}{\sqrt{3}}-\dfrac{8\sqrt{3}}{\sqrt{3}}\)
\(=\dfrac{48-14-8\sqrt{3}}{\sqrt{3}}\)
\(=\dfrac{34-8\sqrt{3}}{\sqrt{3}}\)
\(=\dfrac{34\sqrt{3}-24}{3}\)
