The arc length is the same fraction of the circumference as the central angle is of $360^\circ$. Write that fraction using the given angle.

Once you know what fraction of the circle $120^\circ$ represents, multiply that fraction by the circle's circumference, 30.

In Desmos, type the expression 120/360 * 30 to represent $\dfrac{\text{central angle}}{360^\circ} \times \text{circumference}$ for this problem.

Look at the numeric value Desmos outputs for 120/360 * 30; that value is the length of the minor arc intercepted by the $120^\circ$ angle.

A full circle has $360^\circ$. A central angle of $120^\circ$ is part of that full circle.

Find what fraction of the circle the angle represents:

This fraction tells you what part of the full circumference the arc will be.

Simplify $\frac{120}{360}$:

So the central angle covers $\tfrac{1}{3}$ of the entire circle. That means the minor arc length is $\tfrac{1}{3}$ of the circle's total circumference.

The circle's full circumference is $30$. The arc is $\tfrac{1}{3}$ of this:

So, the length of the minor arc intercepted by the $120^\circ$ central angle is $10$.