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

$$2\times 16=32$$

$$4\times 14=56$$

$$6\times 12=72$$

$$8\times 10=80$$

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.