Given that \(x\) is directly proportional to \(y\) and inversely proportional to \(z\), we can express this relationship as \(x = ky/z\), where \(k\) is the constant of proportionality.

From the given conditions, when \(x = 9\), \(y = 24\), and \(z = 8\), we can find the value of \(k\) as follows:

\(9 = k \cdot 24 / 8\)

Solving for \(k\), we get \(k = 3\).

Now, we can find the value of \(x\) when \(y = 5\) and \(z = 6\) by substituting these values and the value of \(k\) into the equation:

\(x = 3 \cdot 5 / 6 = 2.5\)

So, the value of x when y = 5 and z = 6 is 2.5, which is same as 2\(\frac{1}{2}\).