2. Given that $P$ is a point inside the circle $\odot O$ with radius 15, among all the chords passing through point $P$, 24 chords have integer lengths. Then $O P=$ $\qquad$ .
2. 12 .

Among the chords of circle $\odot O$ passing through point $P$, the diameter is the longest chord, and there is only one; the shortest chord is the one perpendicular to $OP$, and there is also only one. Therefore, there is only one chord each with lengths of $30$ and $18$, and two chords each with lengths of $29, 28, \cdots, 19$, making a total of 24 chords.
By the perpendicular diameter theorem and the intersecting chords theorem, we have
$$
(15+O P)(15-O P)=\frac{18}{2} \times \frac{18}{2} .
$$

Thus, $O P=12$.