The probability of drawing a blue ball from the first bag is \( \frac{3}{8} \), since there are 3 blue balls out of 8 total balls. The probability of drawing a blue ball from the second bag is \( \frac{2}{6} = \frac{1}{3} \), since there are 2 blue balls out of 6 total balls. Since the draws from each bag are independent, the probability that both balls are blue is the product of the individual probabilities: \( \frac{3}{8} \times \frac{2}{6} = \frac{3 \times 2}{8 \times 6} = \frac{6}{48} = \frac{1}{8}. \)