Vacuously true statement

The basic principle is that, for any logical propositions $A$ and $B$ we have:

$~~~~~~A implies [neg A implies B]$

Regardless of the truth value of $B$, if $A$ is true, then the implication $neg A$ implies $B$ is said to be vacuously true.

Here is the truth table (screenshot from Wolfram Alpha):

Here is a proof using a form of natural deduction (screenshot from DC Proof 2.0):

If $A$ is false then $A to B$ is always true, no matter what $B$ is. So just take an $n$ for which the first clause $n > 2$ is false, and then "if $n > 2$ then $B$" is true.

Similarly "if I am a unicorn then pigs can fly" is a true statement, since I am in fact not a unicorn. And "There is some person $A$ such that if $A$ is a unicorn then pigs can fly" is true as long as there is some person who is not a unicorn.

I suspect your confusion may be caused by the given statement looking almost like "There is some $n > 2$ such that $n^2 = 2 n$": in fact students often write "There is some $n$ such that if $n > 2$ then $ldots$ when they mean ""There is some $n > 2$ such that $ldots$". But the two statements are quite different.