。
She's hogging the big room all to herself.
Literal
She [topic-は] big [genitive-な] room [object-を] one-person-monopolize is-doing.
一人占め ('hogging, having all to oneself') is built from 一人 ('one person') + 占め (the ます-stem of 占める 'occupy, take'). 一人占めする ('hog, monopolize') has a slightly negative, possessive flavor — usually said with a trace of resentment or amusement. 大きな is the prenominal form of 大きい — note that 大きい has both regular i-adjective (大きい部屋) and special 大きな (a な-style irregular) attributive forms; 大きな is slightly more lyrical/descriptive than the plain 大きい.