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The phrase "encounter the difficulties" is a correct and usable phrase in written English.
You can use it any time you want to describe a situation when someone is facing challenges, hardships, or problems. For example: "The past year has been difficult for the team, as they have been forced to encounter the difficulties caused by the pandemic."
Exact(4)
You would not expect someone of James Woolsey's professional stature to encounter the difficulties he did in dealing with the Central Intelligence Agency and the Immigration and Naturalization Service.
When we consider system (1.1) by using the classical critical point theory, we encounter the difficulties due to the lack of an appropriate working space.
Many are blessed with never having to encounter the difficulties that life can bring.
While the artist has been playing out a great deal of this new material in nightclubs, as of late, he's indeed had to encounter the difficulties of playing a style that's a bit of an outlier in today's sphere of music that tends to be more sonically approachable.
Similar(56)
When pacifism is defined as anti-warism, we encounter the difficulty of defining war.
We may also encounter the difficulty of an insufficient sample size.
Working in factories and clerical posts for his first five years in the UK, he encountered the difficulties and unhappiness typical for Asian immigrants of the time.
He has tried to be free, and in doing so has encountered the difficulties of what to say, what is acceptable, what is permissible.
When Baber did so, he encountered the difficulty of turning a blueprint into a working weapon.
With the interconnection of DER and change of operation and control modes in the ADN, the traditional feeder automation method encounters the difficulty.
Furthermore, stepwise solid phase peptide synthesis (SPPS) of branching peptides such as MAPs commonly encounters the difficulty of purification to homogeneity and characterization of the final products.
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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