II. (25 points) As shown in Figure 3, $AB$ is the diameter of $\odot O$, chord $CD$ intersects $AB$ at point $E$, and a tangent line is drawn from point $A$ to the circle, intersecting the extension of $CD$ at point $F$. If $CE: DE: DF = 4: 3: 3$ and $AB = 24$, find the length of chord $AC$ and the value of $\sin \angle ACF$.
II. Connect $A D$. Let $C E=4 x, A E=y$.
Then $D F=D E=3 x, E F=6 x$.
By the Pythagorean theorem and the secant-tangent theorem, we have
$$
\begin{array}{l}
A F^{2}=E F^{2}-A E^{2}=D F \cdot C F \\
\Rightarrow 36 x^{2}-y^{2}=30 x^{2} \\
\Rightarrow y^{2}=6 x^{2} .
\end{array}
$$

By the intersecting chords theorem, we have
$$
\begin{array}{l}
A E \cdot B E=C E \cdot D E \\
\Rightarrow y(24-y)=4 x \cdot 3 x=12 x^{2} \\
\Rightarrow 24 y-y^{2}=12 x^{2} .
\end{array}
$$

Combining equation (1), we get $y=8, x=\frac{4 \sqrt{6}}{3}$.
Since $A B$ is the diameter of $\odot O$, and $A F$ is the tangent of $\odot O$, we have
$$
\angle E A F=90^{\circ}, \angle A C D=\angle D A F \text {. }
$$

Since $D$ is the midpoint of the hypotenuse $E F$ of $\mathrm{Rt} \triangle A E F$,
$$
\begin{array}{l}
\Rightarrow D A=D E=D F \\
\Rightarrow \angle D A F=\angle F . \\
\text { Also } \angle A C D=\angle F, \text { then } \\
A C=A F=\sqrt{30} x=8 \sqrt{5} .
\end{array}
$$

In Rt $\triangle A E F$,
$$
\sin \angle A C F=\sin F=\frac{A E}{E F}=\frac{y}{6 x}=\frac{\sqrt{6}}{6} .
$$