A circle has a circumference of 12. It has an arc of length 8/5. what is the central angle of the arc, in degrees?

So lets start out by figuring out what fraction of the whole circumference the arc takes up.

The arc has a length of $\frac{8}{5}$, or $1.6$, out of a circle with circumference $12$.

The arc takes up $\frac{1.6}{12} = \frac{16}{120} = \frac{2}{15}$of the whole circumference. 

This also means that the central angle of the arc takes up $\frac{2}{15}$ of the entire $360$ degree angle.

So the central angle of the arc is $\frac{2}{15}$ of $360$, which is $\boxed{48 \space \text{degrees}}$.