Assuming G is the Central Angle and IG is the radius and J is another point of the circle:
An arclength is simply the length of a part of a circle. So to find the arclength, we take the circumference of a circle (2πr) and multiply it by the percentage of the circle represented by the central angle.
Remember percent can be calculated using is/of. So in your example angle IGJ is 48 degrees of a 360 degree cirlce. So the ratio, or percentage, that represents your specific arclength is (48/360).
Put it together and the arclength formula is (2πr)*(Θ/360)
Substitute your givens, r=6, Θ=48
2π(6)*(48/360) = 1.6π