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If you say "how do you like" something, the response you'll probably get will be along the lines of "poor, okay, good, great" - a qualitative scale.

If you say "what do you think of" something, you may get a broader range of responses -- the acting was good, the story was weak, the scenery was breathtaking, the movie was over-rated, etc.

However, I'd expect to hear it in the past - What DID you think ... ? or How DID you like ...? unless the movie, event, activity, etc. was taking place right at that time. If you are in the intermission of a two-act play, you could ask the question in the present "How do you like the play?" but if you're having coffee afterwards, you'd say "How did you like the play?"
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Hello Jly

The first question asks for an intellectual response.

The second question asks for an emotional response.

MrP
Comments  
Thank you very much!Emotion: smile
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Titanic film is mentioned in our lesson,. all of us like it. the event of the gigantic ship. The song 'My heart will go on 'is listened every where. The youmg love the most the view two couples who straight their hands like the birds in front of the ship.Some people like the blue sapphire of the necklace , a symbol of fidelity People imitate it to wear everywhere.Others like the way the handsome boy went to ship. It's gorgeous! But they don't like the sad story, a lot of dead.

Phuong Ninh
Titanic film is one of my favorite moives, and I'm one of most of people in my country, it's really a touching movie, I watched it when I was studing in high school, But some sencens are as clear as I watched them yesterday. I think its success lies in its telling of the story, they are not only the leading actor and actress who are the foucs, there are many other roles such as the captain, the preist, etc. Maybe they do not have too much part in the movie, however, every of them's performance contributes to the completeness of the movie, without them it may turn out to be no more than a story with romance, and tragedy.

Just my 2 cents
 MrPedantic's reply was promoted to an answer.
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