Please someone help with my maths: For Beatrix's latest art installation, she has fixed a 2 × 2 square sheet of steel to a wall. She has two 1 × 2 magnetic tiles, both of which she attaches to the steel sheet, in any orientation, so that none of the sheet is visible and the line separating the two tiles cannot be seen. As shown alongside, one tile has one black cell and one grey cell; the other tile has one black cell and one spotted cell.

How many different looking 2 × 2 installations can Beatrix obtain?