When you draw the first ball, you have three positive outcomes (the three red balls) and 6 possible outcomes (any of the six balls in the box).
This means that the probabilty of getting a red ball in the first draw is
[tex] \frac{3}{6} = \frac{1}{2} [/tex]
since you return the first drawn ball to the box, the second drawn takes place with the same conditions as the first, exept this time you're looking for a green ball, and thus you only have one positive outcome. So, the probability of getting a green ball is
[tex] \frac{1}{6} [/tex]
The probability of two independent events occuring one after the other is the product of the two probabilities, so the answer to your question is
[tex] \frac{1}{2}\cdot\frac{1}{6} = \frac{1}{12} [/tex]
