What is the folklore story of George Washington crossing the Delaware? Did he throw a silver coin across the river?

You are mixing up two Washington legends, earth. He definitely did cross the Delaware to attack the Hessians in Trenton, New Jersey during the Revolutionary War. The other story, which is probably not true, is that he once threw a silver dollar across the Potomac River. While we're at it, he also didn't chop down a cherry tree and later prove his honesty by saying "I cannot tell a lie."

Across which river did George Washington throw a silver dollar?

The river was not the Potomac or the Delaware, but the Rappahannock River near Fredericksburg, Virginia and Washington threw a piece of slate 'about the size and shape of a dollar,' not a silver dollar, according to Martha Washington's grandson, George Washington Parke Custis. While the story has never been verified, historians concede that the feat is possible. At the site of the Washington family homestead, the Rappahannock measures only 250 feet across, an impressive but not impossible throwing distance.

https://pcunix.medium.com/george-washington-threw-what-across-what-river-910ee016a97e

Yet another geographical fact needs to be clarified. The www.mountvernon.org website states that the Potomac River is over one mile wide at Mount Vernon. That is true but immaterial.

Like the mythical silver dollar, Mount Vernon did not exist at that time either. George grew up about 40 miles downstream. It was reported by Martha's grandson that George threw a stone across the Rappahannock as a boy. The Potomac is approximately five miles across at the George Washington Birthplace National Monument.