If there is no replacement of the balls then it would be:

6/10 * 5/9 = 30/90 = 1/3

There are 6 blue balls, so there is a 6 out of 10 chance of choosing a blue ball first. After you choose the first blue ball, there are 5 blue balls lefts. Thus, there is a 5 out of 9 chance of choosing a blue ball second. Multiply the two and you get 1/3

if there is replacement, then the answer is simply:
6/10*6/10=.36