。
She doesn't like the way I talk.
Literal
She [topic-は] my way-of-talking [subject-が] doesn't-please [explanatory-んだ] [you know-よ].
Three things to notice. First, 話し方 ('way of talking') uses the productive suffix ~方 (read -kata) attached to a verb's masu-stem to form 'way of doing X' — 食べ方 ('way of eating'), 使い方 ('way of using'), 過ごし方 ('way of spending [time]'). Second, the idiom 気に入る ('to like, be pleased with,' literally 'enter the spirit') takes its object with が; the negative is 気に入らない. Third, the casual んだよ stacks the explanatory ~んだ ('it's that ~') with the assertive sentence-final よ — communicating both 'here's the situation' and 'you should know this.'