What is the ruling on working for a carpet company that prints pictures on carpets, with the responsibility of coordinating between the printing press and the company?

The questioner did not clarify the nature of the images, whether they depict living beings or inanimate objects, nor whether they are drawn or photographic. If they are of inanimate objects, there is no harm in them, based on the saying of Ibn Abbas: "If you insist on making images, then you must depict trees or anything that has no soul."

However, if they depict living beings and are drawn by hand, then this is forbidden by the majority of scholars, as it falls under the texts of warning, and working with them is prohibited. Some scholars have permitted images that are incomplete in their creation to an extent that life is not possible, such as a headless image, based on the hadith: "The image is the head, so if the head is cut off, there is no image," and also based on the Prophet's command to 'Aisha to cut up the curtain that had statues on it.

As for photographic images of living beings, there is a difference of opinion among scholars regarding them.