Solution: 28.3 inches

We know that length of the arc is given by θ/360 (2 π r)

(where θ is the angle subtended by the arc and r is the radius of the circle)

Therefore length of arc LMN ≈ 270/360 (2)(3.14)(6)

                                            ≈  28.26  ≈ 28.3 inches (rounding to the nearest tenth)