Answer
$18 \ cm$
Work Step by Step
$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$
or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$
Here, $r$ represents radius and $d$ is diameter.
Thus, equation (b) becomes:
Length $\widehat{AB}=\dfrac{m \widehat{AB}}{360^{\circ}} \times \pi d$
or, $6\pi=\dfrac{120^{\circ}}{360^{\circ}} \times \pi d$
or, $d=18 \ cm$