I am thinking about the many ways to write even numbers for set notation.
I found one that I havent been able to find any confirmations online.
$$\{x\vert x/2 \in\mathbb{Z}\}$$ Is this too simple of an answer?
I did find the other ways to solve but tried simplifying it.
It's not that it's too simple, but it's a little unnatural: For instance, if I extended division by $2$ to apply to some shapes so that, say $\triangle/2=-17$, then it would seem that $\triangle$ should be in your set $\left\{x\mid x/2\in\mathbb Z\right\}$. So your notation requires an underlying assumption that there aren't any weird definitions floating around.
It's a better habit to clearly write where each variable lives, as in $\left\{2k\mid k\in\mathbb Z\right\}$ (common) or $\left\{x\in\mathbb Q\mid x/2\in\mathbb Z\right\}$ (not common, but avoids the problem I mentioned above).
You can see a couple of different-looking ways the set of even naturals might be written in set builder notation at the Examples subsection of the English Wikipedia page for "set-builder notation".