1. **State the problem:** Find the number of solutions to the equation $$-4(x - 5) - 18 = 8 - 4x - 6$$. 2. **Write the equation clearly:** $$-4(x - 5) - 18 = 8 - 4x - 6$$. 3. **Expand and simplify both sides:** - Left side: $$-4(x - 5) - 18 = -4x + 20 - 18 = -4x + 2$$ - Right side: $$8 - 4x - 6 = 2 - 4x$$ 4. **Rewrite the simplified equation:** $$-4x + 2 = 2 - 4x$$ 5. **Compare both sides:** Both sides are identical, meaning the equation holds true for all values of $x$. 6. **Conclusion:** Since the equation is true for every $x$, there are infinitely many solutions. **Final answer:** Infinite number of solutions.