"how did" vs "how" + past tense

Question

What is more correct:

How did you solve the problem?

or

How you solved the problem?

When I use the first variant, people tend to skip the initial word and treat is as if I asked "Did you...". Why?

Answer 1

In a direct question, auxiliary do must be used, to the correct sentence is:

How did you solve the problem?

However, if the question is about the subject, then there is no auxiliary do:

Who solved the problem?

On a side note, in an indirect question or if it is not a question, you don't use the auxiliary do, either:

Now tell me how you solved the problem.
Could you tell us how you solved the problem?

In a negative statement, however, you negate the verb with do not:

Tell us why you did not solve the problem.

Answer 2

The first sentence "How did you solve the problem?" is a perfectly structured and grammatically correct interrogative sentence that is in the past tense.

The second sentence "How you solved the problem?" is bad English. It may be said by some non-native speakers who are just learning English.

Sometimes native speakers speak fast and contract words in speech and even omit letter or words but this isn't the case, however, here is such an example:

• "How d'you solve the problem?" (How do you solve the problem? - the present simple)

The latter sentence can also be mistaken for:

• "Have you solved the problem." (The present Perfect tense)

In addition to my answer, I've heard phrases alike being said by black people in Hollywood films (completely wrong and should be avoided at all costs), one such examples is:

• How's ya done dat?