Final answer:
The sentence requires a modal verb that conveys advice about eating habits. 'Should' and 'ought to' both suggest a recommendation, with 'should' being the best option as it is more commonly used in everyday language. Option b is the correct answer.
Step-by-step explanation:
The question is asking for the correct modal verb to complete the sentence regarding advice on eating habits. In English, modal verbs such as must, should, ought to, and can express different degrees of necessity, obligation, or possibility. The sentence 'You____ cut down on the amount of red meat you eat.' is giving a recommendation rather than a strong necessity or obligation, which would be indicated by 'must' or 'have.' Therefore, the more appropriate modals in this context would be 'should' or 'ought to' which generally suggest advice or a strong recommendation.
The context of diet and health often uses modal verbs like these to give guidance on healthier choices. So, if we consider the nuance of each option: 'must' implies an obligation; 'have cut' is not a modal and it suggests an action that has already been taken; 'can' implies ability or permission; 'should' and 'ought to' imply a recommendation which in this case, is related to health advice.
Taking all these considerations into account, the most suitable answer is 'should' as it is commonly used to give advice. However, 'ought to' is also acceptable as it has a similar meaning. Here, 'should' might be more commonly used in everyday language, while 'ought to' is slightly more formal.
The mention correct option answer in the final answer is 'should'.