1. **State the problem:** Write the fraction $\frac{2}{3}$ as an equivalent fraction with denominator 30. 2. **Formula:** To find an equivalent fraction, multiply numerator and denominator by the same number: $$\frac{a}{b} = \frac{a \times k}{b \times k}$$ 3. **Find the multiplier:** Since the denominator changes from 3 to 30, find $k$ such that: $$3 \times k = 30$$ 4. **Calculate $k$:** $$k = \frac{30}{3} = 10$$ 5. **Multiply numerator and denominator by $k=10$:** $$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}$$ 6. **Check the options:** The equivalent fraction with denominator 30 is $\frac{20}{30}$. **Final answer:** $\boxed{\frac{20}{30}}$