Here are some possible exchanges based on the prompts given:
A: What's the date today?
B: It's the 17th of August. What was the date yesterday?
A: It was the 16th of August.
A: What's the date today?
B: It's the 3rd of June. What was the date yesterday?
A: It was the 2nd of June.
A: What's the date today?
B: It's the 1st of January. What was the date yesterday?
A: It was the 31st of December.
A: What's the date today?
B: It's the 2nd of December. What was the date yesterday?
A: It was the 1st of December.
A: What's the date today?
B: It's the 29th of October. What was the date yesterday?
A: It was the 28th of October.
A: What's the date today?
B: It's the 12th of May. What was the date yesterday?
A: It was the 11th of May.