We cannot assume that p is divisible by 4. We can see that since p2 equals 12 times an integer (q2), p2 is divisible by 12. Since 12 is divisible by 4, p2 is divisible by 4. However, this can only tell us that at most, p is divisible by 2. We can only assume that p is divisible by 4 if we know q is even, which we don't