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The phrase "a problem of how" is correct and usable in written English.
It can be used when discussing the nature or method of addressing a specific issue or challenge.
Example: "The project presents a problem of how to effectively allocate resources while meeting deadlines."
Alternatives: "an issue of how" or "a challenge of how".
Exact(16)
Nevertheless, it presented the Obama administration with a problem of how to respond.
But it was also a problem of how the models were used.
It is always a problem of how to occupy athletes' free time when they are not playing or training.
Nonetheless, perhaps the Apple case can be isolated as a problem of how it drafted the proposal.
While Dynegy needed to delay the vote, it also faced with a problem of how to legally do so.
Again, this wasn't a problem of how he chose to present his beliefs; the problem is with the beliefs.
Similar(43)
Due to a problem of identification, how to estimate the distinct effects of age, time period and cohort has been a controversial issue in the analysis of trends in health outcomes in epidemiology.
For companies, that poses an intriguing opportunity of communicating sustainability to a large audience and a thorny problem of how to do that in an engaging, compelling manner.
Human rights groups said the killing on 13 September in Egypt's Western Desert was an illustration of a deeper problem of how Egypt's military and police use lethal force.
This article concerns a classical problem of how to design an inferential control system for enhancing the performance of distillation composition control.
This article is concerned with a classical problem of how to design an inferential control system for enhancing the performance of distillation composition control.
More suggestions(2)
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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