Answer
See below.
Work Step by Step
The probability of getting 2 is $1/4.$ The probability of getting 2 or 4 is $1/4+1/4=1/2.$ The probability of getting red or green is $1/3+1/3=2/3$. These spinners are independent, hence the probability of getting 2 followed by a 2 or 4 followed by red or green is the multiple of the three, which is $1/4\cdot1/2\cdot 2/3=1/12.$