"How could I" and "how I could"? [closed]

Solution 1:

*[1] I don't know [how could I help you].

[2] I don't know [how I could help you].

*[3] I don't know [how could you do this to me].

[4] I don't know [how you could do this to me].

[2] and [4] are fine. The bracketed elements are subordinate interrogative clauses (embedded questions) functioning as complement of the verb "know".

The meaning is "I don't know the answer to the question 'How could I help you?'" / "I don't know the answer to the question 'How could you do this to me?'"

Subordinate interrogatives don't normally have subject-auxiliary inversion, but [1] and [3] do, and hence they are not acceptable.