How can an α,β-unsaturated ketone tautomerise?
If you have an &#x3b1;,&#x3b2;-double bond next to your carbonyl, a &#x3b3; hydrogen can also take part in tautomerism. Take crotonaldehyde $\ce{H3C-CH=CH-CHO}$:

$$\ce{O=CH-CH=CH-CH3 &lt;&lt;=&gt; HO-CH=CH-CH=CH2}$$

In general, a double bond is able to ‘extend’ the mesomeric properties of a carbonyl compound across two additional atoms. This is known as vinylogous; crotonaldehyde can form a vinylogous enol.

In the specific case of 6,6-dimethylcyclohex-2-en-1-one, these are the two tautomers: