Didst is an old way to say you did — but only with thou, the old singular you: thou didst = you did. You will meet it in the Bible, in Shakespeare, in hymns, and in stories that want an old-time voice. Nobody says it in the street. The -st is the old ending that marked thou (you also see it in hast, dost). Do not put it next to modern you: you didst is wrong. If a play says Why didst thou lie?, it is only Why did you lie? in yesterday's clothes. Learners do not need to speak this; they only need to recognise it on the page.