the year after next
Refers to the year that follows the coming year. Used both as a noun and adverbially.
I plan to graduate from university the year after next.
This project will continue until the year after next.
Compound of 明 (みょう, 'next') + 後 (ご, 'after') + 年 (ねん, 'year'). The reading みょう is an older Sino-Japanese reading of 明 meaning 'next', as also seen in 明日 (みょうにち, 'tomorrow').