I had to translate a question from Russian into English, i did it: “How many years is your sister younger than you?” My teacher’s corrected it into: “FOR how many...?” Is his correction right?
To follow up on @StoneyB's comment -- "for how many years" is measuring the duration of an event; it's not comparing two values.
For example, we can say, "Barack Obama was President of the USA for eight years", or "The Martian was the best-selling book for three weeks". In both of those cases, "for" is required; the sentences don't make sense without it.
The question "for how many years has your sister been younger than you?" is grammatically correct, but it's kind of absurd. If your sister is younger than you, she has been younger for her entire life!