。
She likes to eat fresh raw vegetables.
Literal
She [topic-は] preferring fresh raw-vegetables [object-を] eats.
好んで is the te-form of 好む ('to prefer, to be fond of') used adverbially: 'preferentially, by choice, willingly.' This adverbial pattern is a stock way to mark habitual preference — 好んで読む ('reads by preference'), 好んで聞く ('listens by choice'). 生野菜 ('raw vegetables') as opposed to cooked combines 生 ('raw') + 野菜 ('vegetable'). Raw-vegetable salads have steadily gained ground in Japanese diets since postwar Westernization, but pickled (漬物) and cooked vegetables remain more traditional.