Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 438: 12

$\dfrac{11\sqrt{3}}{6}$

Using the properties of radicals, then, \begin{array}{l} \dfrac{\sqrt{3}}{2}+\dfrac{4\sqrt{3}}{3} \\\\= \dfrac{3(\sqrt{3})+2(4\sqrt{3})}{6} \\\\= \dfrac{3\sqrt{3}+8\sqrt{3}}{6} \\\\= \dfrac{11\sqrt{3}}{6} .\end{array}