。
She has twice as many books as he does.
Literal
She [topic-は] his [genitive-の] two-times [emphatic-も] books [object-を] is-having.
二倍 ('two times, double') uses the productive counter ~倍 (~ばい) for multiples: 三倍 ('triple'), 五倍 ('five-fold'). The も here is the emphatic も attached to a quantity — '(as much as) twice, no less than twice' — heightening the magnitude. Without も it would be neutral ('twice'); with も it stresses surprise or emphasis. 持っている ('be having' = 'have') is the standard ~ている stative for possession.