"How did you managed ..." VS "How did you manage ..." [closed]

Which form is the correct when asking someone how a certain issue was solved:

How did you manage the door problem?

or

How did you managed the door problem?

I'd go with "managed", but a native speaker told me "manage" was the correct form, although she couldn't explain why.

I searched my memory and the internet for what this structure is called, but I could not find it.

Did you [unconjugated verb] is how English is. Unconjugated means the verb, without any -ing, -ed, etc. For instance, you wouldn't say Did you ate my food?, but rather, Did you eat my food?. Typically, if not exclusively, this mechanic is used to turn a statement into a question:

You ate my food. ---> Did you eat my food?

I suppose the word did, being the past tense of do, is taking care of the tense already, so we use the most simple version of the verb, avoiding redundancy.

See this question from the ELL Stack Exchange. You may find that Stack Exchange more useful than this one, anyway.