$T = 6 \to \frac{{2\pi }}{{\left| b \right|}} = 6 \to \left| b \right| = \frac{\pi }{3}$
$\left. \begin{matrix}
\max = 6 \\
\min = -2 \\
\end{matrix} \right\} \to \left\{ \begin{matrix}
\left| a \right| + c = 6 \\
-\left| a \right| + c = -2 \\
\end{matrix} \right. \Rightarrow 2c = 4 \to c = 2 \Rightarrow \left| a \right| = 4$
$y = a\sin bx + c \to y = - 4\sin \frac{\pi }{3}x + 2$