). Simplify \( \left(\frac{2}{3}\right. \) of \( \left.\frac{3}{4}\right)+\frac{1}{12} \)

To simplify \( \left(\frac{2}{3}\right) \) of \( \left(\frac{3}{4}\right) + \frac{1}{12} \), we first calculate \( \left(\frac{2}{3}\right) \times \left(\frac{3}{4}\right) \). Calculating that gives: \[ \frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}. \] Now we add \( \frac{1}{2} \) and \( \frac{1}{12} \) together. To do this, we need a common denominator, which is 12. Rewrite \( \frac{1}{2} \) as \( \frac{6}{12} \): \[ \frac{6}{12} + \frac{1}{12} = \frac{6 + 1}{12} = \frac{7}{12}. \] Thus, the simplified expression is \( \frac{7}{12} \).