。
She thought the problem over carefully for a while.
Literal
She [topic-は] for-a-while [interval-の間] that problem [object-を] carefully-considered.
熟考 (じゅっこう or じゅくこう) is a Sino-Japanese formal compound meaning 'careful consideration, deliberate thought' — built from 熟 ('mature, ripen') + 考 ('think'). Far weightier than 考える alone. The verb implies prolonged, deliberate thinking — turning a problem over rather than glancing at it. The whole sentence has a written, slightly literary feel; in casual conversation you'd say じっくり考えた ('thought it over thoroughly') or よく考えた ('thought it over well'). Common register for biographical narration or news writing about major decisions.