She faced a problem that seemed impossible to understand.
Literal
She [topic-は] understand hard [like-ように] seems problem [to-に] faced.
理解しがたい uses the auxiliary ~がたい ('hard to, difficult to') attached to the masu-stem, expressing inherent difficulty. ~ように思える means 'seems as if.' 直面する (ちょくめんする, 'to face/confront') takes に for the thing confronted.