The first step is to calculate the complementary sets of C and A:
C = {violet, green, orange, red}
C' = U - C
C' = {indigo, blue, yellow}
A = {violet, blue, green, yellow}
A' = U - A
A' = {indigo, orange, red}
Now we just need to find the intersection between C' and A', that is, the elements they have in common:
C' ⋂ A' = {indigo}
So the answer is {Indigo}