1. **State the problem:** We are given that $y$ varies directly with $x$ and the constant of variation is $\frac{2}{3}$. We need to find the value of $x$ when $y=18$. 2. **Formula and explanation:** Direct variation means $y = kx$ where $k$ is the constant of variation. Here, $k = \frac{2}{3}$. 3. **Set up the equation:** $$18 = \frac{2}{3} x$$ 4. **Solve for $x$:** Multiply both sides by the reciprocal of $\frac{2}{3}$ which is $\frac{3}{2}$: $$x = 18 \times \frac{3}{2}$$ 5. **Calculate:** $$x = 18 \times \frac{3}{2} = \frac{18 \times 3}{2} = \frac{54}{2} = 27$$ 6. **Answer:** The value of $x$ when $y=18$ is $27$. **Final answer:** $\boxed{27}$