。
She asked me how many languages I can speak.
Literal
She [topic-は] me [to-に] how-many-languages can-speak [question-か] [object-を] asked.
何カ国語 ('how many languages') is a beautifully compact counter expression: 何 ('how many?') + カ (the counter for countries, written in katakana as a phonetic helper) + 国語 ('national language' = 'language'). Native speakers count 一カ国語, 二カ国語... 何カ国語. 話せる is the potential form of 話す ('speak') — 'can speak.' Pairing the potential with 何 makes a natural 'how many can you do?' question. Languages worldwide are counted with this same カ国語 counter.