。
How old will you be next year?
Literal
Next-year [at-で] how-many-year-old [into-に] become-[explanatory-んです]-[question-か].
来年で ('as of next year') uses で as a temporal cutoff — the reference point at which the age changes. Pairing this with the explanatory ending んですか produces an inquisitive 'so, how old are you turning, then?' tone, slightly warmer and more invested than a flat 何歳になりますか.