Let the radius be r

To keep things simple, model the relationship between the central angle and the arc formed by it as:

angle → length of arc

Keep in mind that the angle and the length of the arc are directly proportional to each other i.e. if one is increased/decreased by a certain factor, the other too will increase/decrease by the same factor

We know that

8 radians → 12 cm

(8/8) radians → (12/8) cm

1 radians → 3/2 cm

1 radians → 1.5 cm

We also know that full angle at the center of a circle is 2π radians (or 360°), and the related arc is just the circumference of the circle i.e. 2π cm

2π radians → 2πr cm

(2π)/(2π) radians → (2πr)/(2π) cm

1 radians → r cm

From the above two relations:

1 radians → 1.5 cm and

1 radians → r cm

Thus r = 1.5 cm

8 radians<----------->12 cm

2π radians<--------->(2π/8) x 12 cm = 3π cm

C = 3π cm

2π r = 3 π

r = 3/2 cm = 1.5 cm