2. As shown in Figure 1, the lengths of the sides of rectangle $A B C D$ are $A B=4$, $B C=8$. The rectangle is folded so that point $C$ coincides with point $A$. Then the length of the crease $E F$ is ( ).
(A) $3 \sqrt{2}$
(B) $2 \sqrt{5}$
(C) $\frac{15}{2}$
(D) $\frac{16}{3}$
2.B.

In Figure 1, connect $A C$ to intersect $E F$ at point $O$.
By the Pythagorean theorem, we know $A C=4 \sqrt{5}$.
When the rectangle is folded so that point $C$ coincides with $A$, we have $E F \perp A C$, then
$$
\begin{array}{l}
\text { Rt } \triangle E O C \backsim \mathrm{Rt} \triangle A B C \\
\Rightarrow \frac{O E}{O C}=\frac{A B}{B C}=\frac{1}{2} \\
\Rightarrow O E=\frac{1}{2} O C=\frac{1}{2} \times 2 \sqrt{5}=\sqrt{5} .
\end{array}
$$

Thus, $E F=2 O E=2 \sqrt{5}$.