If you want to improve your English you ___ work very hard. ?

In the sentence "If you want to improve your English you ___ work very hard," the correct choice is 'D) must.' This choice conveys a strong necessity or obligation. The word "must" implies that working hard is essential for achieving the goal of improving English skills. It signifies that without putting in significant effort, success is unlikely.

Let's briefly consider the other options:

- A) can: This suggests ability or possibility, but it doesn’t convey the required effort needed for improvement.
- B) may: This implies permission or a possibility but lacks the urgency or obligation needed in this context.
- C) are able to: Like "can," it describes capability rather than the necessary effort, failing to communicate the commitment needed.

Using "must" connects directly to the speaker’s intent. It stresses that hard work is not just advisable but essential for English improvement. Therefore, it sets a clear expectation that effort is a non-negotiable part of the learning process, making "must" the most appropriate option in this scenario.