= Solution
Use the presentation $D_6=\langle r,s:r^3=s^2=1, srs=r^{-1}\rangle$. Its subgroup $\langle r\rangle$ is the unique subgroup of order $3$, hence is a <characteristic subgroup>. An <automorphism> must send $r$ to $r$ or $r^{-1}$ and $s$ to one of the three reflections $r^js$. Thus there are at most six automorphisms.
The <center of a group> of $D_6$ is trivial, so conjugation embeds $D_6$ as a group of six <inner automorphisms>. These exhaust the possibilities. Hence \b[every automorphism of $D_6$ is inner].
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