If you omit the "your", and ask a general question, you might get the answer: I like steak a lot but I hate the taste of coffee.Hello.
While preparing a meal for your guest one can ask them:
How do you like your coffee/steak?
Does one always have to say the word "your?"
Could one omit it and say:
How do you like coffee/steak?
For American English, I think I agree with you.I can’t claim to speak for AE speakers, but I think without the ‘done’, it may be taken to mean “Do you like steak?”. Not in BE though.