Although the options that go with this question are not provided, we can still look at how we could rewrite these sentences in more objective ways.
In the case of the first sentence, the sentence is not objective because it assumes that those who do not recycle are "lazy." Moreover, it states that the idea is "great." These are both opinions, not facts. An objective version would look like this:
An idea I have that could improve recycling is to place recycling bins in key places around the city.
On the other hand, the second sentence is not objective because it calls the director "stubborn." An objective version would be:
You will have to convince the director to keep the library open an extra hour each day.
