。
She found that way of his talking thrilling, you know.
Literal
She [topic-は] his [genitive-の] that-kind-of [genitive-の] way-of-talking [at-に] thrill [object-を] felt [explanatory-んです] [you-know-よ].
A casual, conversational sentence with two sentence-final devices stacked: ~んです (explanatory copula, makes the statement feel like an explanation or revelation) + よ (assertion, draws the listener's attention). Together: 'you see, the thing was, she found it thrilling, you know.' しゃべりかた ('way of talking') is built from しゃべる ('chatter, talk') + かた ('way of doing'); a common pattern for forming 'way of X' nouns: 食べ方, 書き方, 考え方. スリル is an English loanword.