Answer
Let $n$ be an arbitrary integer. By the definition of a necessary condition, $n$ being divisible by $2$ is a necessary condition for $n$ being divisible by $6$ means that [$n$ is divisible by $6$] implies [$n$ is divisible by $2$]. Assume that $n$ is divisible by $6$. Then $n=6k=2(3k)$ for some integer $k$. But $3k$ is also an integer, and since $n=2(3k)$, it must be that $n$ is divisible by $2$. Since $n$ was an arbitrarily chosen integer divisible by $6$, it must be that every integer divisible by $6$ is divisible by $2$, i.e., divisibility by $2$ is a necessary condition for divisibility by $6$.
Work Step by Step
Recall from the chapters on logic that "B is a necessary condition for A" and "A is a sufficient condition for B" both mean the same thing as "A implies B."