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She has a strong prejudice against abstract painting.
Literal
She [topic-は] abstract-painting [toward-に対して] strong prejudice [object-を] is-holding.
偏見を持っている ('to hold a prejudice') is the standard expression for having a bias. に対して marks the target of the prejudice. 抽象画 ('abstract painting') combines 抽象 (abstract) and 画 (painting). The sentence is written in a formal, analytical register — the kind of observation you'd read in an essay or character description.