Simplify :

$2\dfrac{1}{4} + 1\dfrac{1}{6} - 1\dfrac{2}{3} ÷ 2\dfrac{2}{3}$ of $3\dfrac{3}{4}$

We have:

$2\dfrac{1}{4} + 1\dfrac{1}{6} - 1\dfrac{2}{3} ÷ 2\dfrac{2}{3}$ of $3\dfrac{3}{4}$

= $\dfrac{9}{4}$ + $\dfrac{7}{6}$ - $\dfrac{5}{3}$ ÷ $\dfrac{8}{3}$ of $\dfrac{15}{4}$ [Converting mixed to improper fraction]

According to BODMAS rule, we solve "of" first

$\begin{array}{ll} = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{3} ÷ \dfrac{8}{3}\times \dfrac{15}{4} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{3} ÷ \dfrac{8 \times 15}{3 \times 4} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{3} ÷ \dfrac{120}{12} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{3} ÷ \dfrac{10}{1} & \text{[Of simplified]} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{3} \times \dfrac{1}{10} & [\text{Reciprocal of } \dfrac{10}{1} \text{ is } \dfrac{1}{10}] \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5 \times 1}{3 \times 10} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{5}{30} \\ = \dfrac{9}{4} + \dfrac{7}{6} - \dfrac{1}{6} \\ = \dfrac{27 + 14}{12} - \dfrac{1}{6} \\ = \dfrac{41}{12} - \dfrac{1}{6} & \text{[Addition simplified]} \\ = \dfrac{41 - 2}{12} \\ = \dfrac{39}{12} \\ = \dfrac{13}{4} & \text{[Subtraction simplified]} \\ = 3\dfrac{1}{4} & \text{[Converting improper to mixed fraction]} \\ \end{array}$

∴ The answer is $3\dfrac{1}{4}$