Gajodhar throws two ordinary dice simultaneously. What is the probability that he shall get two numbers whose product will be an even number? 

Total possible combinations when 2 dice are thrown=6*6=36
Product of 2 numbers is even when either both of them are even or one is even, other is odd.
There are 3 even no.(2,4,6) and 3 odd no.(1,3,5) possible in a dice.
Total combinations when both are even = 3*3 = 9
Total combinations when one is even and other is odd = 3*3(first no. is odd, second even) + 3*3(first no. is even, second odd) = 18
Required probability = $$\frac{\ 9+18}{36}=\ \frac{\ 27}{36}=\ \frac{\ 3}{4}\ $$
Option E is the answer.