4. As shown in Figure 2, the edge length of the regular tetrahedron $ABCD$ is $6 \, \text{cm}$. There are points $E$ and $F$ on edges $AB$ and $CD$, respectively. If $AE = 1 \, \text{cm}$ and $CF = 2 \, \text{cm}$, then the length of line segment $EF$ is $\qquad$ cm.
4. $\sqrt{23}$.
$$
\begin{array}{l} 
\mathbf{F} \mathbf{E}=\mathbf{F} \mathbf{C}+\mathbf{C B}+\mathbf{B E}, \text { note that } C D \perp A B, \text { so } \\
|\mathbf{F E}|^{2}=(\mathbf{F} \mathbf{C}+\mathbf{C B}+\mathbf{B E})^{2} \\
=|\mathbf{F} C|^{2}+|\mathbf{C B}|^{2}+|\mathbf{B E}|^{2}+ \\
2(\mathbf{F C} \cdot \mathbf{C B}+\mathbf{F C} \cdot \mathbf{B E}+\mathbf{C B} \cdot \mathbf{B E}) \\
= 4+36+25+2\left(2 \times 6 \times \cos 120^{\circ}+0+6 \times 5 \times \cos 120^{\circ}\right) \\
= 23 .
\end{array}
$$
$$
\text { Therefore, } E F=|E F|=\sqrt{23}(\mathrm{~cm}) \text {. }
$$