Imagine you are trying to cover the whole (modified) board with tiles each two squares long – so they can go either vertically or horizontally and will always cover one black and one white (yellow) square.
You can use a brush to make two-square lines to get a feel for the problem, and undo your attempts with ctrl+z keys.
One you have had a few goes, sit back and try to figure out WHY it is not possible to achieve the goal. There is a sound, logical reason for it which will be obvious once you have either discovered it or been told.
Good luck, and enjoy the process!