Answer
$f(-\frac{4\pi}{5}=1$ because having a period of $\pi$ means that the sine function will repeats its value for every interval of $\pi$.
Since $\frac{6\pi}{5}-2\pi=-\frac{4\pi}{4}$, then
$f(\frac{6\pi}{5})=f(-\frac{4\pi}{5})$
Work Step by Step
Note that $-\frac{4\pi}{5} = \frac{6\pi}{5}-2\pi$.
If a sine function has a period of $\pi$, then the function's value repeats (or the same) for every interval of $\pi$.
Thus, if $f(\frac{6\pi}{5}=1$, then
$f(\frac{6\pi}{5}-2\pi)=f(\frac{6\pi}{5} - \frac{10\pi}{5})=f(-\frac{4\pi}{5})=1$$
