。
She blushed to the roots of her ears.
Literal
She [topic-は] ear [possessive-の] base [up-to-まで] red became.
耳のつけ根 ('the root/base of the ear') is the spot where the ear joins the head — the まで ('up to, all the way to') extends the redness from a partial blush to a fully crimson face. This is a vivid, slightly novelistic image. つけ根 (付け根) more commonly comes up for joints — 足のつけ根 ('hip area, where the leg meets the body'), 首のつけ根 ('base of the neck'), 翼のつけ根 ('where wing meets body'). Combined with 赤くなる ('turn red, blush'), the phrase paints intense embarrassment.