Answer: D. $24$

Explanation:1. Understand the given equation: The equation is $x^2 - 24x - 8 = 0$. This is a quadratic equation in the form $ax^2+bx+c=0$.

2. Recall the formula for the sum of the solutions of a quadratic equation: For a quadratic equation $ax^2+bx+c=0$, the sum of its solutions (roots) is given by $-\dfrac{b}{a}$.

3. Identify the coefficients $a$ and $b$: In the equation $x^2 - 24x - 8 = 0$: $a = 1$ $b = -24$ $c = -8$

4. Calculate the sum of the solutions: Sum of solutions $= -\dfrac{b}{a} = -\dfrac{-24}{1}$ Sum of solutions $= -(-24) = 24$.

5. Compare with the given options: [A] $0$ [B] $4$ [C] $8$ [D] $24$ Our result matches option D.

6. Conclusion: The sum of the solutions to the given equation is $24$.