1. **State the problem:** Calculate the product of $2 \frac{3}{4}$ and $-4 \frac{2}{3}$. 2. **Convert mixed numbers to improper fractions:** $2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$ $-4 \frac{2}{3} = -\frac{4 \times 3 + 2}{3} = -\frac{14}{3}$ 3. **Multiply the fractions:** $$\frac{11}{4} \times -\frac{14}{3} = -\frac{11 \times 14}{4 \times 3} = -\frac{154}{12}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 154 and 12, which is 2. $$-\frac{\cancel{2}77}{\cancel{2}6} = -\frac{77}{6}$$ 5. **Convert the improper fraction back to a mixed number:** Divide 77 by 6: $77 \div 6 = 12$ remainder $5$. So, $$-\frac{77}{6} = -12 \frac{5}{6}$$ **Final answer:** $$2 \frac{3}{4} \times -4 \frac{2}{3} = -12 \frac{5}{6}$$