Method 1: List all possible cases

Step 1: Make a vertical list of even integers whose sum is 18

$$ 2+16=18 $$

$$ 4+14=18 $$

$$ 6+12=18 $$

$$ 8+10=18 $$

Step 2: Multiple each to find the largest product

$$ 2\times16=32 $$

$$ 4\times14=56 $$

$$ 6\times12=72 $$

$$ 8\times10=80 $$

Therefore 80 is the answer.

Method 2: Notice that the product of 2 even integers must be even

Only 80 is an even number among the choices, and therefore is the correct answer.