A prime number is a number whose factors a 1 and that number alone. For example, the number 11 is a prime number since its factors are only the numbers 1 and 11 (i.e. itself), whereas the number 12 is not a prime number since it has other factors besides 1 and 12 (e.g. 2, 3, 4, and 6).

(1) y>4!
This tells us that y is any number greater than 4!. Since the numbers greater than 4! include both prime and non-prime numbers, this statement is insufficient.

(2) y = 11!-12
This statement gives us the precise value of y (since we can calculate the numerical value of 11!-12), and thus determine whether y is prime. Statement (2) is therefore sufficient.

The answer is thus (B).