1. **State the problem:** Calculate the product of the fractions $\frac{3}{4}$ and $\frac{2}{7}$. 2. **Formula:** To multiply two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{3}{4} \times \frac{2}{7} = \frac{3 \times 2}{4 \times 7} = \frac{6}{28}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 6 and 28, which is 2, and divide numerator and denominator by 2: $$\frac{6}{28} = \frac{\cancel{6}^3}{\cancel{28}^{14}} = \frac{3}{14}$$ 5. **Final answer:** $$\frac{3}{14}$$