How would you describe the general direction of diffusion across the membrane of this cell?

Carbon dioxide would diffuse out of the cell.

One of the first things that will happen to this cell is carbon dioxide will flow out of the cell. This happens because carbon dioxide is a waste product, and there is more carbon dioxide inside this cell than there is outside the cell. The little ovals show carbon dioxide. Furthermore, there would be a movement of a protein into the cell.

Proteins are needed to make many things, and cells like to keep an equal balance between things inside the cell and outside the cell - becoming isotonic if you will. So, one protein molecule will move into the cell. On that same principle of balance, two carbon dioxide molecules will move out, putting three on each side of the cell membrane.