Which four border states remained loyal by the Union?

That would be:

Maryland

Delaware

Kentucky

Missouri

West Virginia also was a member of the Union that allowed slavery. However, it was one of two new states formed during the Civil War, and is probably not the "correct" answer for this one. West Virginia Seceded from Virginia when Virginia seceded from the Union. Nevada was the other state formed during the Civil War. It separated from Utah Territory, and became a state on October 31, 1864 (8 days before the federal election) in order to ensure President Lincoln's victory.