For the non re-entrant condition mentioned, the answer should be option C.
If the thread has to acquire the lock → work on critical section → release lock, then a single thread cannot create deadlock, so x should be 2.
coming to y, if y is 1, then the circular dependency is not happening i.e say the threads are T1 and T2
and the lock be l1.
Say T1 acquires l1 i.e T1 → l1. But T1 would enter critical section and thus one of T1 and T2 is not locked thus deadlock is not happening.
Taking y to be 2
Say T1 → l1 and T2 → l2. Now both T1 and T2 are in a deadlock trying to acquire l2 and l1 respectively.
Now for the interesting case of re-entrant code i.e where the thread can leave critical section without releasing the lock and try to aquire again, then both x and y can be 1, since T1 would try to aquire l1 two times, with the first time being a success the second time would definitely be a failure as the lock has not been released.