Hume raises many significant arguments in this second half of his book. He addresses the idea that virtues are useful as they are the most desired description of a man. He says that every man desires to be described as virtuous because virtue is the greatest compliment afforded man. He then explains why it is that usefulness (utility) causes pleasure. Hume says that when something proves useful, it gives direct benefit to the person describing it as useful, and it is from this application to self (self love) that the pleasure arises.
In the next section, Hume discusses the “qualities useful to ourselves.” He makes the point that it is less about the quality in question and more about the degree of the quality, as “no quality…is absolutely either blameable or praise-worthy.” He explains this point using different qualities.
Continuing in his discussion of agreeable qualities, Hume then presents qualities which he claims are immediately agreeable. He uses cheerfulness as an example, but also discusses dangerousness as the reverse: an immediately disagreeable quality. Courage and tranquility are two more examples he uses. I found his arguments here to be particularly convincing.
Section 8 discussed a few of the qualities that others immediately find agreeable. Ingenuity, good manners and politeness, and decency provided support for his arguments here. I had a bit of difficulty understanding exactly how Hume distinguished between the qualities immediately agreeable and immediately agreeable to others. I am not sure I understand well enough to be able to distinguish should I be handed a list and asked to sort them into their separate categories.