The phrase "able to know the difference" is correct and usable in written English.
You can use it when discussing someone's capacity to distinguish between two or more things.
Example: "Children at a young age are often not able to know the difference between right and wrong."
Alternatives: "capable of discerning" or "able to distinguish."
On Thursday, a psychiatrist said Mr. Holmes, 27, was indeed able to know the difference and was legally sane.
"For instance, I have been running the largest group of private companies in Europe, but I had never been able to know the difference between net and gross.
It's what we call configuration rather that customization -- and it takes a developer brain to be able to know the difference.
Audiences are now better able to know the difference between a guessed animated expression of anger and a science based animated depiction of anger.
You should be able to know the difference between OS X 10.4.x and OS X 10.5.x, know about iLife and iWork, and be able to tell the difference between a MacBook and a MacBook Pro.
Lessons conveying science and religion as two distinct ways of knowing were similar to the following; "Students will be able to know the differences and similarities between evolutionary science and religious dogmas.
"Students will be able to know the differences and similarities between evolutionary science and religious dogmas.
But those aspects we cannot know merely by being conscious of them are part of our conscious experience in just the same way as those aspects we are supposed to be able to know; the difficulty is specifying a principled difference between the two.
The difference in accuracy means a civilian will be able to know the position of a car, ambulance or skier within about the dimensions of a tennis court.
How, I wondered, could someone able to comprehend those written words not have the sense to know the difference between ice cream and rubber?
