Final answer:
When z is divided by 6, the remainder is 4, which means z can be written as 6k + 4. Therefore, when z is divided by 2, the remainder will always be 0, because 4 is divisible by 2 with no remainder.
Step-by-step explanation:
When z is divided by 6, the remainder is 4, which means that z can be expressed as z = 6k + 4 for some integer k. To find the remainder when z is divided by 2, we consider the expression 6k + 4. Since 6k is divisible by 2 for any integer k, the remainder solely depends on the 4 in 6k + 4. Dividing 4 by 2 gives a remainder of 0, implying that no matter what the value of k is when z is divided by 2, the remainder will always be 0.