1. **State the problem:** We need to calculate $3 \times \frac{4}{21}$ and simplify the result. 2. **Write the multiplication:** $$3 \times \frac{4}{21} = \frac{3}{1} \times \frac{4}{21}$$ 3. **Multiply the numerators and denominators:** $$\frac{3 \times 4}{1 \times 21} = \frac{12}{21}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 12 and 21, which is 3. 5. **Divide numerator and denominator by the GCD:** $$\frac{\cancel{3} \times 4}{\cancel{3} \times 7} = \frac{4}{7}$$ 6. **Final answer:** $$\boxed{\frac{4}{7}}$$