A boy has 4 red , 6 yellow and 3 green marbles. In how many ways for Marbles of the same color are indistinguishable?

Huh? Your question is incomplete.

UPDATE:
Let's first consider the number of permutations if all 13 marbles were distinguishable. That would just be 13! = 13 x 12 x 11 x ... x 3 x 2 x 1 = 6,227,020,800

Now for every permutation, there will be 4! = 24 arrangements that are identical except for the fact that the red balls are rearranged. So we need to divide by 24 to account for the fact that they are indistinguishable from each other.

Likewise for the 6 yellow balls there are 6! = 720 identical arrangements, so divide by 720 to account for that.

And finally for the 3 green balls, we divide by 3! = 6 to account for those identical arrangements.

The final formula is:
13! / (4! 6! 3!)
= 6227020800 / (24 * 720 * 6)
= 60,060

Answer:
60,060 ways