Use this below code : 

public class SimpleFileMove 
{ 
    static void Main() 
    { 
        string sourceFile = @"C:\Users\Public\public\mindstick.txt"; 
        string destinationFile = @"C:\Users\Public\private\mindstick.txt"; 
        // To move a file or folder to a new location: 
        System.IO.File.Move(sourceFile, destinationFile); 
        // To move an entire directory. To programmatically modify or combine 
        // path strings, use the System.IO.Path class. 
        System.IO.Directory.Move(@"C:\Users\Public\public\mindstick\", @"C:\Users\Public\private"); 
    }

use following code for deleting file and directory both.

        try
            {
                var FilePath=@"C:\\Temp\\ABC.TXT";
                if (System.IO.File.Exists(FilePath))
                {
                    System.IO.File.Delete(FilePath);
                    Directory.Delete(FilePath.Substring(0, FilePath.LastIndexOf('\\')));
                }
            }
            catch (Exception ex)
            {
                Debug.WriteLine(ex.Message);
            }