Probability is the number of desirable choices divided by the number of total choices. The first time you draw a sock you want blue, so it is 18/(10+18) or 18/28. You can simplify that to 9/14. The second time you want another blue sock, but there is one less blue sock in the drawer and there's one less sock in the drawer. The probability of getting a blue sock is 17/27. We multiply these 2 fractions, (9/14)x(17/27) to get the final answer, 153/378. We can simplify both of these numbers by 9 to get the simplified answer, 17/42.
Hope this helped!