Question: User: $\frac{2}{3}$ by $\frac{3}{4}$
1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $\frac{3}{4}$.
2. **Formula:** To multiply two fractions $\frac{a}{b}$ and $\frac{c}{d}$, use the formula $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}.$$
3. **Apply the formula:** $$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4}.$$
4. **Calculate numerator and denominator:** $$\frac{6}{12}.$$
5. **Simplify the fraction:** Both numerator and denominator share a common factor of 6. Cancel the 6:
$$\frac{\cancel{6}}{\cancel{12}} = \frac{1}{2}.$$
6. **Final answer:** The product of $\frac{2}{3}$ and $\frac{3}{4}$ is $\frac{1}{2}$.