難問を

a difficult problem

→ 難問
phrase Rare #32,205
a difficult problem 難問 means “difficult problem” or “tough problem,” and を marks it as the direct object of a verb. This phrase is normally followed by a verb such as 解く (to solve) or 解決する (to resolve).
JA: 彼女はその難問を解いた。
EN: She solved that difficult problem.

このようにして彼はその難問を解いた

This is how he solved the difficult problem.

彼は難問をうまく処理するだろう

He will handle the difficult problem well.

彼は難問を解決した

He solved the difficult problem.

こんなふうにして私はその難問を解いたのです

This is how I solved that difficult problem.

彼女は難問をうまく処理するだろう

She’ll handle the difficult problem well.