Answer
$r=8$ units
Work Step by Step
Step 1: The formula to be used here is $s=r\theta$ where s is the length of the arc intercepted, r is the radius and $\theta$ is the central angle of measure in radians.
Step 2: $s=r\theta$
Step 3: $6\pi=(r)(\frac{3\pi}{4})$
Step 4: $6=(r)(\frac{3}{4})$
Step 5: Multiplying both sides by 4, $6\times4=r\times\frac{3}{4}\times4$
Step 6: $24=3r$
Step 7: Multiplying both sides by $\frac{1}{3}$, $24\times\frac{1}{3}=3r\times\frac{1}{3}$
Step 8: $r=8$ units
