You should use a two-population z test under the following circumstances:
D) The standard deviation is known and n > 30.
A two-population z test is appropriate when you have two independent samples and you know the population standard deviations. Additionally, the sample size should generally be greater than 30 to satisfy the conditions for using the z test, as this is when the sampling distribution of the sample mean is approximately normal according to the Central Limit Theorem.
The other options mentioned (A, B, and C) either suggest situations that would require a different test (like a t-test) or don't meet the necessary conditions for a z test.