The probability of an even number on one die is 1/2, as is the probability of an odd number. Thus, the probability of two odd numbers (no even numbers) is (1/2)*(1/2) = 1/4. That makes the probability of at least one even number be 1-1/4 = 3/4.
The two dice can be (odd, odd), (odd, even), (even, odd), or (even, even). If they are (odd, odd) or (even, even), the result will be an even number. Thus the probability of two dice totaling an even number is 2*(1/2)*(1/2) = 1/2.