1. **State the problem:** Solve the equation $$\frac{6x}{x - 2} = \frac{4x + 4}{x - 2}$$. 2. **Important note:** The denominator $$x - 2$$ cannot be zero, so $$x \neq 2$$. 3. **Since denominators are the same and not zero, set the numerators equal:** $$6x = 4x + 4$$ 4. **Solve for $$x$$:** $$6x - 4x = 4$$ $$2x = 4$$ $$x = \frac{4}{2} = 2$$ 5. **Check if $$x=2$$ is valid:** Since $$x=2$$ makes the denominator zero, it is not a valid solution. 6. **Conclusion:** There is no solution to the equation. **Final answer:** There is no solution.