She didn't have much trouble finding the answer to the problem.

Literal

She [topic-は] problem [possessive-の] answer [object-を] find-out [purpose-のに] not-very labored-not.

あまり苦労しなかった ('didn't struggle much') uses the softened negation あまり~ない. 見つけ出す (みつけだす, 'to find out, discover') is a compound verb combining 見つける + 出す.