When you use backslash (\), java assumes that you are going to use an escape character. If you want to print that line you should probably use the method below and it should work. And you are using a string inside another one so you should use different types of inverted commas for both to tell the compiler that yeah there is a string inside another one. Otherwise the compiler will assume the middle inverted comma to be the closing one.
You can escape each and every escape character. If you notice I have used a backslash before inner inverted commas (" ") and every other backslash (\). Using a backslash before any escape character escapes it. So this should work.
System.out.println("Path = \"C:\\Users\\Public\"");
I hope now you can print your required output.