The angle ∠CAB sweeps out some fraction of ⊙A's full 360∘, and subsequently the same fractional part of ⊙A's circumference. To find what the fraction is, we can divide ∠CAB by 360:
m∠CAB360=55360=1172
So, ∠CAB sweeps out 1172 of the circle's circumference.
The circumference of any circle is equal to the product of π and the diameter d of the circle, which is itself equal to twice the radius, 2r. Here, we're given r=AC=12, so the circle's circumference is π⋅2(12)=24π.
So, the length of the arc BC=1172⋅24π=24π⋅1172
24 and 72 both have the factor 24 in common, so we can reduce down to
11π3
And we're done.