Example of play; rule holding difficulty:
Domain Difficulty: The DDC is 10 + province level + the new holding level.
Modifiers: Prosperity; Stability; Advantage [Law] – Does not apply to ruling law holdings; Advantage [Guild] – Applies to ruling trade holdings; Hardiness [Law or same holding; guild holdings also apply to ruling trade].
This looks rather complicated, but really it isn't:
Base DDC is pretty simple. Just add together the province level and the new holding level; to rule a holding to lvl 4 in a province 6 is 10 + 4 + = DDC 20.
Stability - Almost always applies to all domain actions, so no shocker there.
Prosperity - Pretty straightforward. A well-run province is easier to do business in; applies equally to all regents in this case.
With a prosperity of Loyal, you get a -1 reduction. With a prosperity of, lets say Content, you get another -2, for a total of -3. DDC now 17.
A little bit more complicated, but only a little
Advantage [Law] - If you're ruling any non-law holding the DDC is reduced by 2 if you've got half or more law. The reduction is 4 points if you've got all the law. Remember that a law (0) in a province (0) counts as 1/2 law.
Advantage [Guild] - Same as above, but only applicable to trade holdings. Note that if you've got both guild and law, you might qualify for the +2 synergy bonus.
So lets say your a guilder improving your guild from 3 to 4. Luckily you're the royal guild of the realm and get support from the law ruler, who has sufficient law to get you the 2 point decrease. DDC is now 15.
Hardiness [Law or same holding] - Follows the same rules as advantage...
The other major guild has a guild (2) in the province. That's not enough to qualify for Hardiness, so DDC stays at 15.
Now anyone who has a holding or is the province rule can start spending influence to further affect the DDC.