The phrase "demonstrate an understanding of" is correct and usable in written English.
You can use it when discussing someone's ability to grasp or comprehend a particular concept or subject matter.
Example: "In order to pass the exam, students must demonstrate an understanding of the key principles covered in the course."
Alternatives: "show comprehension of" or "exhibit knowledge of".
Be able to talk through a news story and demonstrate an understanding of the issues raised.
But Mr. Wildhorn has yet to demonstrate an understanding of what makes a Broadway musical sing.
The most important goal at this stage is to demonstrate an understanding of the other person's point of view.
They then individually create a work of their own that pays homage to a Rauschenberg to demonstrate an understanding of his aesthetic sensibility.
To be accepted on a course, you'll need to demonstrate an understanding of social work and an awareness of the challenges facing those in the profession.
For a third grader who fails a standardized math test, she said, that means being able to demonstrate an understanding of three-dimensional objects and being able to apply the appropriate mathematical operations to problems.
Francis has demonstrated an understanding of that in practical action.
Though likely apocryphal, the story nonetheless demonstrates an understanding of the principle behind parachuting.
The strategy demonstrates an understanding of what drives many investment decisions, said Meir Statman, professor of finance at Santa Clara University and author of What Investors Really Want.
'SEXY BEAST' -- The first-time director Jonathan Glazer demonstrates an understanding of drama and performance that tends to elude most directors who make the move from video to film.
Then he told a story about how he once blew the mind of Francis Crick, over lunch, when he explained to him that the Indian belief in reincarnation demonstrated an understanding of deep space and the history of the universe.
