Answer
$\sqrt{123}$
Work Step by Step
The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Hence here: $d=\sqrt{(2\sqrt3-(-\sqrt3))^2+(\sqrt6-5\sqrt6))^2}=\sqrt{(3\sqrt3)^2+(-4\sqrt6)^2}=\sqrt{27+96}=\sqrt{123}$