4. As shown in Figure 4, on the side $AB$ of rectangle $ABCD$, there is a point $E$, and $\frac{AE}{EB}=\frac{3}{2}$. On the side $DA$, there is a point $F$, and $EF=18$. When the rectangle is folded along $EF$, point $A$ lands on point $G$ on side $BC$. Then $AB=$ $\qquad$
$4.5 \sqrt{6}$