To solve the quadratic equation \(y - 11\sqrt{y} + 24 = 0\), we can use a substitution to simplify the equation. Let's make the substitution \(u = \sqrt{y}\), which means \(u^2 = y\).

Now the equation becomes:

\[u^2 - 11u + 24 = 0\]

We can factor the quadratic equation:

\[(u - 8)(u - 3) = 0\]

Setting each factor equal to zero:

\[u - 8 = 0 \quad \text{or} \quad u - 3 = 0\]

Solving for \(u\) in each case:

\[u = 8 \quad \text{or} \quad u = 3\]

Now, substitute back for \(u\) to find the corresponding values of \(y\):

\[u^2 = y\]

\[(\sqrt{y})^2 = y\]

So:

\[y = 8^2 = 64\]

\[y = 3^2 = 9\]

The solutions for \(y\) are \(y = 64\) and \(y = 9\).