tan Y = 8/15 is correct. This 8/15 = opp side / adj side.
cos X is actually 8/17, which does not belong among the correct answers here.
tan X = 15/8 = opp / adj is correct.
sin Y = 8/17 is correct. That's opp / hyp.
cos Y = 8/17 is incorrect. Here, cos Y = adj / hyp = 15/17.
In summary, the correct statements are:
tan Y = 8/15
tan X = 15/8
sin Y = 8/17