1. **Stating the problem:** Calculate the value of $$p = \frac{-\frac{2}{3} \times \frac{3}{5} + \frac{5}{2} \times \frac{3}{5} \times \frac{1}{6}}{-\frac{3}{4} \times \left(\frac{2}{3} + \left(-\frac{5}{6}\right)\right)}$$ and then find the reciprocal of $p$. 2. **Calculate the numerator:** $$-\frac{2}{3} \times \frac{3}{5} = -\frac{2 \times 3}{3 \times 5} = -\frac{6}{15} = -\frac{2}{5}$$ $$\frac{5}{2} \times \frac{3}{5} \times \frac{1}{6} = \frac{5 \times 3 \times 1}{2 \times 5 \times 6} = \frac{15}{60} = \frac{1}{4}$$ Sum numerator terms: $$-\frac{2}{5} + \frac{1}{4} = -\frac{8}{20} + \frac{5}{20} = -\frac{3}{20}$$ 3. **Calculate the denominator:** First, inside the bracket: $$\frac{2}{3} + \left(-\frac{5}{6}\right) = \frac{2}{3} - \frac{5}{6} = \frac{4}{6} - \frac{5}{6} = -\frac{1}{6}$$ Multiply by $-\frac{3}{4}$: $$-\frac{3}{4} \times \left(-\frac{1}{6}\right) = \frac{3}{24} = \frac{1}{8}$$ 4. **Calculate $p$:** $$p = \frac{-\frac{3}{20}}{\frac{1}{8}} = -\frac{3}{20} \times \frac{8}{1} = -\frac{24}{20} = -\frac{6}{5}$$ 5. **Find the reciprocal of $p$:** The reciprocal of $p = -\frac{6}{5}$ is: $$\frac{1}{p} = -\frac{5}{6}$$ 6. **Match with options:** Options are: (a) $\frac{1}{4}$ (b) $-\frac{1}{8}$ (c) $-8$ (d) $16$ None of these exactly match $-\frac{5}{6}$, so the reciprocal is $-\frac{5}{6}$. **Final answer:** The reciprocal of $p$ is $-\frac{5}{6}$.