Explanation:

Number of balls = 6 + 5 + 8 = 19 
Exhaustive number of cases = Ways of selecting 4 balls out of 19

19C4 = 19 x 18 x 17 x 16 /1 x 2 x 3 x 4 = 3876

Favourable number of cases = Selecting 4 red balls or any two green balls out of the four 

6C2 + 5C2  x 14C2 = 6 x 5 x 4 x3 /1 x 2 x 3 x 4 + 5 x 4/2 x 14 x 13 /2

= 15 + 910 = 925

Required probability = 925 /3876

Hence, option 2 is the correct answer.