1. **State the problem:** Solve for $y$ in the equation $$\frac{y + 4}{6y} - \frac{4}{9} = \frac{1}{y}.$$\n\n2. **Identify the common denominator:** The denominators are $6y$, $9$, and $y$. The least common denominator (LCD) is $$\text{LCD} = 18y.$$\n\n3. **Multiply both sides by the LCD to clear denominators:**\n$$18y \times \left(\frac{y + 4}{6y} - \frac{4}{9}\right) = 18y \times \frac{1}{y}.$$\n\n4. **Distribute multiplication:**\n$$18y \times \frac{y + 4}{6y} - 18y \times \frac{4}{9} = 18y \times \frac{1}{y}.$$\n\n5. **Simplify each term:**\n$$\cancel{18y} \times \frac{y + 4}{\cancel{6y}} = 3(y + 4),$$\n$$\cancel{18y} \times \frac{4}{9} = 8y,$$\n$$\cancel{18y} \times \frac{1}{\cancel{y}} = 18.$$\n\n6. **Rewrite the equation:**\n$$3(y + 4) - 8y = 18.$$\n\n7. **Expand and simplify:**\n$$3y + 12 - 8y = 18,$$\n$$-5y + 12 = 18.$$\n\n8. **Isolate $y$:**\n$$-5y = 18 - 12,$$\n$$-5y = 6.$$\n\n9. **Divide both sides by $-5$:**\n$$y = \frac{6}{\cancel{-5}} \times \frac{\cancel{-1}}{1} = -\frac{6}{5}.$$\n\n10. **Check for restrictions:** $y \neq 0$ and $y \neq -\frac{4}{1}$ (from denominators). Our solution $y = -\frac{6}{5}$ is valid.\n\n**Final answer:** $$y = -\frac{6}{5}.$$