Step 1: Note the goal.
We want to decide whether $n$ is even. We test each statement separately.
Step 2: Think about what even means.
A number is even if it divides cleanly by $2$.
Step 3: Try Statement I alone.
If $n$ is divisible by $4$, then $n = 4k$, and $4k$ is always a multiple of $2$. So $n$ must be even. Statement I alone works.
Step 4: Try Statement II alone.
If $n$ is divisible by $8$, then $n = 8m$, which is also always a multiple of $2$. So $n$ must be even. Statement II alone works too.
Step 5: Compare the two findings.
Each statement on its own already settles the question with a clear yes.
Step 6: Decide sufficiency.
Since either one is enough by itself, we do not need both.
Step 7: State the answer.
Either statement alone is sufficient. \[ \boxed{\text{Either statement alone is sufficient}} \]