Find the third proportional to $2\dfrac{2}{3}$ and 4.

Let the third proportion to $2\dfrac{2}{3}$ and 4 be x,

$\Rightarrow 2\dfrac{2}{3} : 4 = 4 : x \\[1em] \Rightarrow \dfrac{8}{3} : 4 = 4 : x \\[1em] \Rightarrow \dfrac{\dfrac{8}{3}}{4} = \dfrac{4}{x} \\[1em] \Rightarrow \dfrac{8}{12} = \dfrac{4}{x} \\[1em] \Rightarrow x = \dfrac{4 \times 12}{8} \\[1em] \Rightarrow x = 6.$

Hence, third proportional to $2\dfrac{2}{3}$ and 4 is 6.