What is the ruling on a web designer who places images of women in his designs if it is difficult to avoid doing so or to find alternative images?

Even if the woman's face and hands are not considered 'awrah (parts of the body that must be covered), the aforementioned pictures often show a part of the woman's 'awrah. Therefore, it is not permissible for you to place these pictures on the website if they show anything from the 'awrah, even if displaying the picture is not the primary purpose.