There are ten buildings in the residential compound.
Tips
usage
栋 is specifically for buildings — 一栋楼, 一栋别墅, 一栋大厦. It cannot be used for rooms or floors, only whole buildings. The character originally meant 'ridgepole' (the main beam of a roof).
Wood radical on the left — the indexing radical. A ridgepole is the main wooden beam at the apex of a traditional Chinese roof, holding the whole structure together. From 'ridgepole' the meaning extended to 'whole building,' which is why 栋 became the measure word for buildings.
Right side 东 supplies the sound, with the tone shifting to 4th in 栋. Same phonetic in 冻 (dòng, freeze) and 动 (dòng, move) — a clean dōng/dòng family. The simplified 东 replaced traditional 棟's 東 phonetic, preserving the same sound clue.