Many examples show to to ask "would you like" but how do you ask a question in the past tense, for example, "did you like going to the movie with ...."
asking about a past event

ksfarmer
June 21, 2016

Paul-Weber
July 14, 2016
You can ask: "Mochtest du es?"= "Did you like it?" or "Hast du es gemocht?"="Have you liked it?"
To work with your examples:
"Mochtest du es mit Peter ins Kino zu gehen?"= "Did you like going to the movies with Peter?" This is not only a completed action in the past tense but suggests that the person has been to the movies with Peter several times in the past.
"Hast du es gemocht mit Peter ins Kino zu gehen?"= "Have you liked going to the movies with Peter?"
A more common way how to ask is: "War es schön mit Peter ins Kino zu gehen?"= "Was it nice going to the movies with Peter?"
Hope this helps!
Paul
To work with your examples:
"Mochtest du es mit Peter ins Kino zu gehen?"= "Did you like going to the movies with Peter?" This is not only a completed action in the past tense but suggests that the person has been to the movies with Peter several times in the past.
"Hast du es gemocht mit Peter ins Kino zu gehen?"= "Have you liked going to the movies with Peter?"
A more common way how to ask is: "War es schön mit Peter ins Kino zu gehen?"= "Was it nice going to the movies with Peter?"
Hope this helps!
Paul