Answer
The graph does not necessarily have symmetry with respect to the polar axis, the line $\theta =\frac{\pi }{2}$, or the pole.
Work Step by Step
We look for symmetry by making the following substitutions:
(a) $\theta \to - \theta$ :$$r=2+3\sin 2(- \theta ) \quad \Rightarrow \quad r=2-3\sin 2 \theta$$Thus, the graph does not necessarily have symmetry with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$-r =2+3\sin 2 (-\theta ) \quad \Rightarrow \quad r=-2+3\sin 2 \theta$$Thus, the graph does not necessarily have symmetry with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$-r =2+3\sin 2 \theta \quad \Rightarrow \quad r=-2-3\sin 2 \theta$$Thus, the graph does not necessarily have symmetry with respect to the pole.
