The statement "X is directly proportional to y and inversely proportional to z" means $x \propto y$ and $x \propto \frac{1}{z}$. Combining these gives $x \propto \frac{y}{z}$. We write this as an equation using a constant $k$: $x = k \cdot \frac{y}{z}$.

We are given that $x = 9$ when $y = 24$ and $z = 8$. Substitute these values to find $k$:

$$9 = k \cdot \frac{24}{8}$$ $$9 = k \cdot 3$$ $$k = \frac{9}{3} = 3$$

So the law connecting the variables is $x = 3 \cdot \frac{y}{z}$.

Now we need to find $x$ when $y = 5$ and $z = 6$. Substitute into the formula:

$$x = 3 \cdot \frac{5}{6}$$ $$x = 3 \cdot \frac{5}{6} = \frac{15}{6} = \frac{5}{2}$$ $$\frac{5}{2} = 2\frac{1}{2}$$

So the correct answer is D) $2\frac{1}{2}$.

Textbook reference: Comprehensive Mathematics for Senior Secondary Schools, p. 92