The eggs of the parasite live in the soil which is contaminated by feces and also when the eggs pass through feces then the layer of the egg is stained golden-brown by the bile.
To answer this question you should know what bile stained eggs. Bile stained eggs are the eggs which are stained golden-brown by the bile.
Now start with the option A i.e., Roundworm. Roundworms are the parasites which live inside the intestine. These parasites survive by living in the other creature. The eggs of the roundworms live in the soil which is contaminated by feces. The uterine wall makes the thick outer layer of the eggs and when the eggs pass through excreta, the mammillated layer is stained golden-brown by the bile.
The next option is B i.e., Hookworm. Hookworms are the parasitic roundworms which cause helminthiasis infection. Eggs of the hookworms are passed in the feces of the infected person. Their eggs are not stained by bile. Therefore, this cannot be the correct answer.
Moving to the option C i.e., Guinea worm. It causes guinea-worm disease. When a person drinks water which contains water fleas infected with the guinea worm larvae then the person becomes infected by this disease. Eggs of this worm are also not stained by the bile and thus this option is also not the correct one.
Last option is D i.e., Threadworm. These are the parasitic worms which infect the large intestine of human beings. These worms lay their egg usually at night around the anus of the infected person. These eggs are also not stained by the bile. Hence from all the above options, it is clear that Eggs of Roundworms are bile stained.
Thus, the correct answer is option A i.e, Roundworms.
Note: Roundworms are the parasites which live in the intestine and their eggs live in the contaminated soil. These eggs are stained by the bile when they get passed through the excreta and there is no such staining by bile in any other parasite. Therefore only eggs of roundworms are stained by bile.