。
She cooks chicken to suit my taste.
Literal
She [topic-は] my preference [to-に] meet [so-as-to-ように] chicken-meat [object-を] cooks.
Note the writing 会う where 合う is expected — 'to meet (a person)' versus 'to fit / suit (a thing).' Both are pronounced あう, and homophones of this kind are a common source of writing slips even for native speakers. The intended phrase 好みに合う means 'to suit one's taste'; 会う is firmly limited to meeting people. ~ように attached to a non-volitional verb expresses purpose ('so that / in such a way that'). 鳥肉 is an alternate writing of the more common 鶏肉 ('chicken meat') — 鶏 specifies the bird is a chicken; 鳥 is broader (poultry/bird), but in food contexts almost always means chicken anyway.