1. **State the problem:** Solve the equation $$2 + \frac{4}{y - 4} = \frac{6}{y - 4}$$ for $y$. 2. **Identify the domain:** The denominator $y - 4$ cannot be zero, so $y \neq 4$. 3. **Isolate the fractions:** Subtract $\frac{4}{y - 4}$ from both sides: $$2 + \frac{4}{y - 4} - \frac{4}{y - 4} = \frac{6}{y - 4} - \frac{4}{y - 4}$$ 4. **Simplify the fractions:** $$2 = \frac{6 - 4}{y - 4} = \frac{2}{y - 4}$$ 5. **Solve for $y$:** Multiply both sides by $y - 4$: $$2(y - 4) = 2$$ 6. **Use cancellation:** $$\cancel{2}(y - 4) = \cancel{2}$$ which simplifies to $$y - 4 = 1$$ 7. **Find $y$:** $$y = 1 + 4 = 5$$ 8. **Check domain:** $y = 5$ is valid since $5 \neq 4$. **Final answer:** $$y = 5$$