。
She became a master of flower arranging.
Literal
She [topic-は] ikebana [possessive-の] master became.
生け花 (いけばな) is the Japanese art of flower arranging — literally 'living flowers.' 大家 (たいか) means 'master' or 'authority' in a field — someone who has achieved the highest level of expertise. Note the reading: 大家 is たいか when meaning 'master/expert,' but おおや when meaning 'landlord.'