These issues lie in the CV joints (constant velocity joints) that allow the axle to 'bend'.
They can fail as a result of road debris puncturing the rubber bellows. Their lives can also be shortened by constant full-lock maneuvering.
Costs depend on the type of replacement parts used. Most expensive are new OEM axles. Factory rebuilt axles are also available and are a viable alternative to new. Last in desirability are aftermarket replacement parts...much cheaper but they have a spotty reliability record.
That said, I'm wondering if they want to replace both sides because they can't actually tell which one is bad? (In other words, they are guessing...a BAD sign.)
Perhaps a 'second opinion' from an independent Honda specialty shop is warranted. Or, another dealer that will honor your warranty.