The problem says


    180*(n-2) = 24*(360/n).     (1)


Here "n" is the number of sides (vertices)  of the polygon;

left side is the sum of interior angles;  right side is 24 times the exterior angle.



Simplify equation (1). First step is to cancel the factor 180 in both sides.


    n-2 = 24*(2/n)

    n^2 - 2n = 48

    n^2 - 2n - 48 = 0

    (n-8)*(n+6) = 0.


Of the two roots, only positive root  n= 8 makes sense.


ANSWER. Number of sides is 8.  The polygon is a regular octagon.