1. Look at this yellow hat. You will look good in it.
I am not sure. I think I would prefer .... brown hat.
You should use 'a' here because you are talking about any brown hat.
2. What is .... time?
It is half past four.
You should use 'the' because 'time' is uncountable.
3. Can I get you anything?
I will have .... cup of tea, thank you.
You should use 'a' because you are not talking about a particular cup.
4. How about some cake?
No thanks, I am on .... diet.
You should use 'a' because you do not say which diet you are on.
5. Can we have some music?
Sure. Do you like .... Beatles?
You should use 'the' because it is the name of a pop group.
6. It's so cold and rainy.
Yes, .... weather has been bad this week.
You should use 'the' because you are talking about the weather at a specific time.