1. **State the problem:** We have the equation $$3|x - 8| = k$$ where $$k$$ is a constant. We want to find the value(s) of $$\frac{k}{3}$$ such that the equation has exactly one solution. 2. **Recall the properties of absolute value equations:** - The equation $$|x - a| = b$$ has two solutions if $$b > 0$$. - It has exactly one solution if $$b = 0$$. - It has no solution if $$b < 0$$ because absolute value cannot be negative. 3. **Rewrite the equation:** $$3|x - 8| = k \implies |x - 8| = \frac{k}{3}$$ 4. **Analyze the number of solutions based on $$\frac{k}{3}$$:** - If $$\frac{k}{3} > 0$$, there are two solutions. - If $$\frac{k}{3} = 0$$, there is exactly one solution. - If $$\frac{k}{3} < 0$$, there are no solutions. 5. **Conclusion:** For the equation to have exactly one solution, $$\frac{k}{3}$$ must be 0. **Final answer:** (C) 0 only