Z cannot be #6 because it must take place earlier than Y per rule 4. Please see below for the full setup:
The game requires us to determine the order of the auditions and whether they are recorded or not. The game involves six singers - K L T W Y Z. Two of their auditions are recorded - K & L and four not recorded - T W Y Z.
R U __ __ __ __ __ __ 1 2 3 4 5 6
The following rules apply:
(1) The 4th audition cannot be recorded, the fifth must be.
This rule allows us to infer that the fifth audition must be either K or L, and 4th is neither K nor L.
R X U X __ __ __ __ K/L __ 1 2 3 4 5 6
(2) W audition must take place earlier than two recorded auditions. This rule tells us that W must audition before both K & L, thus W cannot be #6. and audition #1 cannot be recorded since W (unrecorded) must precede both recorded auditions.
W > K & L
(3) K audition must take place earlier than T audition. This rule tells us that K cannot be #6, and allows us to infer that #5 and #6 auditions cannot both be recorded because it would leave no space for T. Combined with the previous rule, another interesting inference is that W can only be #1 and #2 since we know that #4 and #6 are unrecorded auditions, the earliest the second recorded audition could be is #2 -K or L, hence we can infer that W must be #1 or #2, and K/L (second recorded audition) must be #2 or #3.
We can also infer that if K is #5, then T must be #6 and that T cannot be #1 or #2 because T must precede K and the earliest K could be is #2.
R X U X X X /K/L /W /W /K/L __ K/L __ 1 2 3 4 5 6 ~T ~T ~K ~W
(4) Z audition must take place earlier than Y audition.
Z> Y
This rule allows us to infer that Z cannot be #6 and Y cannot be #1. Combined with the previous rules we can also infer that #1 must be either W or Z, and #6 must be T or Y.
R X U X X X /K/L Z/W /W /K/L __ K/L T/Y 1 2 3 4 5 6 ~T ~T ~Y ~Z
We can overall see that the only possible auditions that could take place sixth are either T or Y.
