1. **State the problem:** Find the permissible values of $x$ for the expression $$\frac{2x}{6x+6} + \frac{x-8}{12x-12}.$$\n\n2. **Identify restrictions:** The denominators cannot be zero because division by zero is undefined.\n\n3. **Set denominators not equal to zero:**\n- For $6x+6 \neq 0$, solve $6x+6=0$ which gives $x=-1$.\n- For $12x-12 \neq 0$, solve $12x-12=0$ which gives $x=1$.\n\n4. **Conclusion:** The permissible values of $x$ are all real numbers except $x=-1$ and $x=1$ because these values make the denominators zero and the expression undefined.