There's a ratio that holds for arc lengths:
[tex]\dfrac{\text{arc length}}{\text{measure of angle subtended by arc}}=\dfrac{\text{circumference}}{\text{one full revolution}}[/tex]
Denote the arc length by [tex]L[/tex] and the angle subtended by it by [tex]\theta[/tex]. Then given a circle of radius [tex]r[/tex], this relation says
[tex]\dfrac L\theta=\dfrac{2\pi r}{2\pi}=r\implies L=r\theta[/tex]
So, the arc length in this case is simply
[tex]L=4\text{ cm}\times3=12\text{ cm}[/tex]
