Identify the Term-to-Term Rule: Analyzing the 8, 6, 4, 2 Sequence

To solve this problem, we'll approach it step by step:

Step 1: Identify the sequence pattern.
The sequence given is 8, 6, 4, 2, ... Each term is 2 less than the previous one.

Step 2: Determine the common difference.
The difference between any two consecutive terms (e.g., 6 - 8, 4 - 6) is $-2$.

Step 3: Use the formula for the $n$-th term of an arithmetic sequence.
For a sequence with first term $a_1 = 8$ and common difference $d = -2$, the $n$-th term can be calculated using:

$a_n = a_1 + (n-1) \cdot d$
This gives us:

$a_n = 8 + (n-1)(-2)$
$= 8 - 2n + 2$
$= -2n + 10$

Therefore, the rule for the sequence is $a_n = -2n + 10$.

By comparing this with the given options, the correct choice is:

$-2n + 10$