How many structural isomers does 1,2-dimethyl-cyclohexane have?
My teacher said there is one structural isomer

I think (hope) you are talking about stereo isomers (i.e. same Lewis structure, different substance).
There are two ways of counting. Either you can ask &quot;How many substances are stereo isomers of cis-1,2-dimethylcyclohexane?&quot; Or you can ask &quot;How many stereo isomers exist of 1,2-dimethylcyclohexane?&quot;. The correct answers are off by one.
This is like asking &quot;how many siblings do you have&quot; vs. &quot;how many siblings are there in your family (including you)&quot;.

How many structural isomers does 1,2-dimethyl-cyclohexane have?

The molecular formula for this substance is $\ce{C8H16}$. There are lots of substances with that formula but different Lewis structure.