Proving complexity by reduction using strongly NP-hard problem
I will assume that your definition is the one on Wikipedia.

We wish to prove that $X$ is strongly NP-Complete. Here's how you do that. First, show that $X$ is strongly NP$^1$. Next, find a strongly NP-Complete problem $Y$ and reduce $Y$ to $X$. That is, provide an algorithm which takes an instance $y$ of $Y$ and produces $f(y)$ such that if $y\in Y$ then $f(y)\in X$ and otherwise, if $y\not\in Y$ then $f(y)\not\in X$.

I remember in which way to reduce a problem (was it $X$ to $Y$ or $Y$ to $X$?) by framing it as a conversation which I've laid out here in this other answer(link): someone challenges me by saying $X$ is easy. Then I say, nonsense, if $X$ were easy, then I could solve very hard problem $Y$. And then I show how to do that: I take an instance of $Y$, rewrite it into an instance of $X$, and then you're done. You've shown that $X$ is at least as hard as $Y$, so we write $Y\leq X$.

$^1$ best I can figure, strongly NP means it has logarithmically-sized certificates