Arc length is a fraction of the whole circumference. That fraction is $\dfrac{\text{central angle}}{360}$ when the angle is in degrees.

Plug $r = 3$ and central angle $120^{\circ}$ into the arc length formula $\dfrac{\theta}{360} \cdot 2\pi r$ and simplify step by step.

In Desmos, type the expression (120/360)*2*pi*3. Look at the numeric output that Desmos gives you, and then match that value to one of the answer choices.

For a circle with radius $r$, the circumference (distance all the way around) is

The length of a minor arc with central angle $\theta^{\circ}$ is the same fraction of the circumference as $\theta^{\circ}$ is of a full $360^{\circ}$:

Here, the radius is $r = 3$ and the central angle is $\theta = 120^{\circ}$. Substitute these values into the formula:

First simplify the fraction:

Now substitute this back into the expression:

Multiply $2\pi \cdot 3 = 6\pi$, so

So, the length of minor arc $\widehat{AB}$ is $2\pi$, which matches choice A.