In direct answer to the question on your test paper:
Q. What's your favourite colour?
A. My favourite colour is......
I would have to say the correct answer from your multiple choice is (c) white with green.
This is because the part of the answer that has been written for you only allows for one colour to be stated as your favourite.
"White but pink" is not something I have ever heard. It sounds more like indecision or an inability to describe a single colour properly.
"White and pink" are two colours.
It would not be unusual for someone to answer the question "what is your favourite colour?" with:
I like white and pink.
My two favourite colours are white and pink.
The question may assume you have one favourite but if you have two favourites or your preference is always for a colour combination then sure, answer with two! You just wouldn't phrase it as "my favourite colour is white and pink". Your test paper has already given you this part of the sentence, so your answer must be one colour. Likewise in your other example of the "black and white cat" a person may ask you what single colour your cat is, assuming it is a single colour such as black or white. This does not prevent you from answering correctly that it is "black and white".
"White with green" suggests a mix of colours, what some may describe as an "off-white" or a "very pale green", and this would be accepted as being a single colour.