The phrase "a difficult time explaining" is correct and usable in written English.
You can use it when discussing challenges in conveying information or clarifying a concept to someone.
Example: "I had a difficult time explaining the complex theory to my classmates."
Alternatives: "struggling to explain" or "having trouble articulating".
Rogelio had a difficult time explaining.
"The Greeks certainly will have a difficult time explaining the deal to their voters," he said.
But, like other Army psychiatrists, Stokes has a difficult time explaining the Army's squeamishness on the subject.
"The athlete will have a difficult time explaining the spikes and troughs of patterns in their blood.
The Romney campaign's leaders, along with Mr. Rove, will have a difficult time explaining themselves in private to big donors feeling angry and betrayed.
Those who focus on the black experience during the Civil War have a difficult time explaining, or even admitting, the strange allure of Haiti.
"It was a difficult time", explained Fahrudin to the Bosnian weekly newspaper Slobodna Bosna years later.
A view about chance which does not include this connection will have a very difficult time explaining why the principles of direct and inverse inference (i.e., inference from actual statistics of outcomes to chance, and vice versa) in statistical hypothesis testing work at all (Hacking, 1965; Ismael, 1996; Eells, 1983).
Still, the Bannas had a more difficult time explaining some aspects of Raad's disappearance.
The Republican party is going to have a very difficult time explaining their opposition to financial reform to swing voters.
"The other explanations have a difficult time … explaining the timing and magnitude of the increase we saw in 2015 and continue to see in some cities in the current year," Rosenfeld said.
