The arc marked in red is a quarter of the circle's circumference.
Hence the arc marked red subtends an angle of 90degrees.
[tex]\begin{gathered} \text{Given an arc that subtends }\theta\text{ at the center of with radius r} \\ \end{gathered}[/tex][tex]\text{arc length, l = }\frac{\theta}{360}\times2\pi r[/tex]
In our case
[tex]\theta=90^o,\text{ r = 6m}[/tex][tex]l=\frac{90}{360}\times2\pi(6)=\frac{1}{4}\times2\pi(6)=3\pi m[/tex]
