Well, like any other challenge roll in the game, you imagine what your character is doing to handle the situation or how they are responding to it, and then you pick your traits that apply to roll.
Remember that if you don't have two, you can always imagine d4 traits on the fly. So, if you are grappling with "Ale is consumed. Much ale." and you have literally nothing in your pre-selected traits to roll that applies, you can always imagine, say, "d4 Staggering through the headache" and "d4 Hair of the dog that bit ya" and roll those to see what comes out on top.
Have fun with it! If your character's traits just simply don't apply to the situation, that's not great for your die rolling, sure, but it's a fun creative opportunity. That's a situation where your character is really out of their element, so you can come up with weird responses, lucky coincidences, miraculous providence, sudden appearances of old friends or rivals, or obscure backstory to flesh out your character a bit. (And maybe that die will even come out on top!)
Also remember you're always responding to two challenge dice, so if you can't think of much that fits "Ale is consumed. Much ale.", you can simply lean into whatever the other challenge die is and respond to that, and if "Ale..." comes out on top, well, whatever you were trying to do was derailed because of your hangover. You didn't try to respond to it, nor did you have anything particularly able to counter it...and it got ya!
Bottom line: Just pick dice that will make for interesting story, whether they're dice your character already has or d4's to fill out what doesn't apply.