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"That approach will never work, Odair."
"And why not?" It's evident from the tilt of Finnick's head, the arch of his eyebrow, that he's not exactly used to being told being the smoldering Finnick Odair, District Four Victor won't accomplish whatever it is in this instance he's attempting to. And it's further evident from the hard look Haymitch gives him that Finnick ought to just quit while he's ahead and listen to the damned guy. It's not like he mentored her through one set of games or anything.
Most of the rest of their exchange is silent. Glances exchanged over the top of the girl's head. The boy's as well, seeing as Mellark knows almost less than her. But he is preoccupied with Katniss, and Haymitch would honestly be surprised if he was truly aware of anyone else but her at the moment. Stupid kids and their love.
Finnick seems to get it, however. At least, Haymitch hopes he gets it because if they mess this up there is no second chance with this particular one.
Later, Katniss is visibly disgruntled by her interaction with Finnick. Haymitch can only roll his eyes at her. The girl on fire never learns.