。
Books take up most of his room.
Literal
Books [subject-が] his [attributive-の] room [attributive-の] greater-part [object-を] occupy-[ongoing-ている].
占める ('to occupy, take up, hold') is a transitive verb for space or proportion. 大部分 ('the greater part, most') is a Sino-Japanese noun. The ている here marks the resulting ongoing state — 'are in a state of occupying' — which English handles with the simple present 'take up.'