Beginning of your Challenges

You could do an intrigue challenge with Sansa Stark, but Jaime would just defend with Lannisport Steward and win the challenge. It may be worth forcing your opponent to kneel his last standing character, but let's save Sansa Stark for later (if you read the cards in your hand, you may be able to figure out why).

Let's indulge in House Stark's strength instead - the military challenge! Initiate a military challenge with Eddard Stark by kneeling him:

You initiate a military challenge with Eddard Stark

Your opponent has no standing characters with the military icon. As a result, you win the challenge unopposed. Your opponent has to kill some of his characters!

How many does he have to kill? Look at the claim on your plot, Respect of the Old Gods. The rightmost number is a 2, so Jaime must kill 2 of his characters.

He says he will kill Feuding Clanswoman and Cersei Lannister. Feuding Clanswoman goes to the dead pile, but instead of killing Cersei Lannister, he just discards the attachment on her. What just happened?

Read that attachment - Gilded Plate. It can be discarded to save the attached character from being killed or discarded. So Cersei Lannister doesn't die. . . for now. But your opponent has to discard Gilded Plate - and the card also specifies that your opponent has to lose 2 power from his house. He only has 1, so all his power is gone.

You also get some bonus effects. You won the challenge unopposed, so you claim 1 power for your House. In addition, read the text on Eddard Stark. He has the keyword renown: what that means is after he participates in a challenge and wins, he claims 1 power for himself. This power counts towards your win total; however, if Eddard Stark is killed or discarded, you lose that power. Renown works on attack or defense.

Eddard Stark also has a special ability on his card: after you win a military challenge, he stands and gets +2 STR until the end of the phase. So stand him back up!

You win the military challenge, claim unopposed and renown, and stand Eddard Stark

What next? The intrigue challenge is still out, for reasons mentioned before, but you can do a power challenge. If you win a power challenge, you can move X power from your opponent's House card to your own, where X is your claim..

Let's do a power challenge with Eddard Stark. You can use him again because he is standing. Jaime cannot defend, so you claim 1 power for your house. Eddard Stark has renown, so he claims a power as well. Finally, if your opponent had 2 or more power, you would move 2 power to your House - but he doesn't, so that effect fizzles. The renown and unopposed still give you a net gain of 2 power, though.

You win a power challenge and claim unopposed and renown

Your challenges are over. Things aren't looking so bad: you have the stronger characters, and you have 4 power to your opponent's 0. Time for the Dominance phase!