Answer
$d=9
\text{ units}
$
Work Step by Step
Using $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ or the Distance Formula, then the distance, $d$, between the given points $(
-\sqrt{3},4\sqrt{6}
)$ and $(
2\sqrt{3},\sqrt{6}
)$ is
\begin{array}{l}\require{cancel}
d=\sqrt{(-\sqrt{3}-2\sqrt{3})^2+(4\sqrt{6}-\sqrt{6})^2}
\\\\
d=\sqrt{(-3\sqrt{3})^2+(3\sqrt{6})^2}
\\\\
d=\sqrt{9\cdot3+9\cdot6}
\\\\
d=\sqrt{27+54}
\\\\
d=\sqrt{81}
\\\\
d=\sqrt{(9)^2}
\\\\
d=9
\text{ units}
.\end{array}
