4 balls can be selected from 10 balls in ${10_{C}}_{4}$ ways.
2 red balls can be selected from 6 red balls in ${6_{C}}_{2}$ ways.
2 green balls can be selected from 4 green balls in ${4_{C}}_{2}$ ways.
hence probability= (${6_{C}}_{2}$ *${4_{C}}_{2}$)/${10_{C}}_{4}$ = 3/7
Answer: (B)