Yes, they should be assumed identical only when explicitly stated so.

Hi Gunjan
The question asks, "In how many different ways can 3 red balls, 2 blue balls and 4 yellow balls be arranged so that the balls of the same color come together."
Therefore, all the balls of the same color must be together

The number of ways in which we can arrange the colors = $$3\times\ 2\times\ 1$$ = 6   (i)
(Basically, first we will pick one out 3 colors to be placed first, then we will pick one out of 2 colors to be placed second, and then we will be left with just 1 color that will come in last

Now, we have figured out the number of ways in which the colors can be arranged. Now, we must figure out in how many ways can the colored balls be arranged for each color.
Number of ways in which the 3 red balls can be arranged = $$3\times\ 2\times\ 1$$ = 6   (ii)
(Same as above, first we will pick one out of 3, then one out of remaining 2, then we will be left with 1)
Number of ways in which the 2 blue balls can be arranged = $$2\times\ 1$$ = 2   (iii)
(We will pick any 1 out of the 2, and then will be left with just 1)

Number of ways in which the 4 yellow balls can be arranged = $$4\times\ 3\times\ 2\times\ 1$$ = 24   (iv)
(We first pick 1 out of 4, then 1 out of the remaining 3, then 1 out of the remaining 2, then we will be left with 1)
From (i), (ii), (iii), (iv):
Total number of ways the balls can be arranged = $$6\times6\times2\times24$$ = 1728
Hope this helps, please let us know if any doubts persist!