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"faces a difficulty" is a correct and usable phrase in written English.
It is often used to indicate that someone is encountering a problem or challenge. Example: "John faces a difficulty every morning when he has to wake up early for work."
Exact(10)
But Russia faces a difficulty, too.
But Mr. Clinton faces a difficulty that the ordinary writer -- even the ordinary presidential writer -- doesn't.
But about to go back on tour, the comedian faces a difficulty: kids want to see him live.
However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions.
Netanyahu faces a difficulty in trying to reassure Washington that he is interested in a deal with the Palestinians while not appearing weak at home.
From the point of view of physics, the use of the internal quantum yield is perfectly justified but faces a difficulty in experimental determination of the photon flux absorbed in the emitter.
Similar(50)
Students are facing a difficulty either in understanding native speakers or in producing native-like English (accent/pronunciation).
Abelard's position was shown to face a difficulty by Alberic of Paris in the 1130s.
Despite its explicitly modal character, the Modal Approach does face a difficulty similar to the one faced by the Question Approach.
But besides the epistemic problem, advocates of ideas faced a difficulty accounting for the origins of the contents of our very ideas of external objects.
Charging for public services faces a number of difficulties.
More suggestions(20)
faces a challenge
encounters a difficulty
faces a dilemma
exists a difficulty
faces a complication
faces a burden
faces a hurdle
faces a predicament
faces a barrier
faces a crisis
experience a difficulty
faces a challenging
facing a difficulty
faces a life
faces a conundrum
faces a slowdown
faces a fitness
faces a variety
faces a drubbing
faces a choice
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com