The phrase "difficulty they face" is correct and usable in written English.
You could use it in any context where you are referring to the challenge or obstacle that someone or something is confronted with. For example, "The students had to work hard to overcome the difficulty they face in completing the project."
One difficulty they face is the cussed tendency of biological things to evolve.
The difficulty they face is indicated by a story from the book.
That judgment is made by the board of directors, and auditors have to agree with it.The difficulty they face is that most companies fund their operations in part through borrowing, which can stretch from simple overdrafts to huge syndicated loans.
Too many questions are not even on the table, such as poor levels of pay in the teaching profession, head teachers' lack of freedom to recruit their own staff, and the difficulty they face getting rid of poor teachers.
But their unwillingness to impose steeper reductions also reflected the severe difficulty they face in slashing spending on the wide scale demanded by some Republicans, especially Tea Party-backed freshmen elected partly on a promise of fiscal restraint.
The difficulty they face is in reconciling China to their need for an American comfort blanket.This is a symptom of a broader problem: the belief, common on both sides, that China can rise only at America's expense.
The refugees outlined their struggles in Syria and the difficulty they faced in relocating to a new country.
However, as she tried to learn English herself, she realized the difficulty they faced and thus began to encourage her children to socialize with people no matter their language or race.
Many participants discussed the difficulty they faced finding work in the neighborhoods in which they lived.
Many supervisors in this setting expressed that lack of AN motivation was the main difficulty they faced in impacting performance.
Some respondents reported the difficulty they faced offering free maternal health services in the presence of budget constraint, and claimed that it was not realistic in actual implementation.
