I'm running The Brotherhood Without Banners agenda.Now I have no brotherhood char on the play. Then can I initiate a power challenge? And if so, what happen if I win? Nothing happen or discard power from my opponent's house card? And why?

sky_cuson said:

The BwB Agenda says that you must place any power you claim for or move to your house on a Brotherhood character instead. If you don't control any, any power that would be claimed remains unclaimed, and any power you could move remains unmoved.

You can initiate Power challenges like normal. Deadly, Renown and card effects keyed to the challenge happen as normal, but you can't claim power for unopposed (or any power claim card effects), and the claim for the challenge doesn't happen. The power simply stays on the losing defender's house card.

The power isn't discarded either, because moving power from your opponent's house card is a single action. It doesn't happen in two steps (first he discards, then you gain), but rather in one step. If the power can't move anywhere to, it is not moved from the house card either.