This question can be as much about morals than anything else and they want to know how you would convince a client to take your suggestions as well as how far you would go. Don’t dwell on the difficult client aspect, stick to your persuasions and letting your expertise speak for itself. You could make suggestions such as:

I would create an opportunity for the client to accompany me to test or view things for themselves to give them a better first-hand experience that allows me to better explain my recommendations.