'has difficulty discerning' is correct and can be used in written English.
It is used to indicate that someone has difficulty making a distinction between things or understanding something. For example, "The student has difficulty discerning the difference between an adjective and an adverb."
Ferman said that last year, even as renovations were concluding, the U.S.T.A. still had difficulty discerning "construction costs from operating expenses" and underestimated the costs of utilities and maintenance.
Young children, even would-be Rembrandts, might have difficulty discerning the fine distinctions in component images, and most teenagers would probably be more excited about a role-playing or an action game.
In Connecticut, a task force on liquefied natural gas appointed by Gov. M. Jodi Rell is nearly ready to send her its report, laying out the project's advantages and disadvantages for Connecticut, but members said they were having difficulty discerning whether the Broadwater gas would benefit the state.
(This is why Facebook has been testing the use of a "satire" tag on shared news stories – Facebook users apparently have difficulty discerning truth from bias and falsehoods).
Most editors had difficulty discerning the difference between the bottled and canned Coke.
Although I am a veteran debate observer, I often have difficulty discerning a clear victor when I watch these programs.
Oldenburg claimed to have straddled Warspite once, though her gunners had difficulty discerning the British battleship in the growing haze.
However, parents and moreover children can have difficulty discerning trustworthy sources of online information from those that are not.
Authors sometimes have difficulty discerning if a specific relationship could be considered as a potential competing financial interest.
