"faced major difficulties" is correct and usable in written English.
You can use it when you want to indicate that a person or group of people experienced a significant challenge. For example, "The team faced major difficulties when attempting to complete the project on time."
These children faced major difficulties growing up in one of the country's poorest municipalities.
Outside the US, investment in conventional oil and gas projects remains subdued and Birol said the world faced "major difficulties" if investment was not stepped up.
Mark Higson, Royal Mail's managing director, said: "Like other essential services, we have faced major difficulties with items moving in and out of areas most impacted by the snow and ice, particularly Scotland and the north-east of England.
The Prussians faced major difficulties in capturing these castles as they were accustomed only to battling in open fields.
At the same time, the Pakistani officials said they were facing major difficulties in efforts to monitor the militants' activities.
Unless they are "patrial" or are in one of the special permit free categories - doctors, dentists, businessmen, and journalists posted to Britain - they will face major difficulties.
Within two years of the communist victory, however, it became clear that Vietnam would face major difficulties in realizing its goals.
Using data mining methods, this paper presents a new means of identifying freshmen's profiles likely to face major difficulties to complete their first academic year.
Even though construction and demolition waste (CDW) is the bulkiest waste stream, its estimation and composition in specific regions still faces major difficulties.
A $1.4 billion project to build the world's most powerful neutron source has fallen several months behind schedule during its first year of construction and is facing major difficulties in obtaining further construction funds.
And yet it was clear Le Pen faces major difficulties in the presidential race as party members and supporters gathered in the traditional heartlands of the Côte d'Azur for her party conference this weekend, where many sat in straw hats and boaters bearing ribbons marked "Marine 2017".
