She can speak both English and German.

Literal

She [topic-は] English [and-と] German [genitive-の] both [subject-が] can-speak.

The ~と~の両方 frame names two languages and packages them as 'both.' Here the predicate is the simple potential 話せる (from 話す), and potentials in Japanese typically take their 'object' with が rather than を — Xが話せる, 'can speak X.' The shift from 話す/を to 話せる/が is one of the cleaner illustrations of how potential forms promote the underlying object to subject status grammatically.