Pixel/cm or pixel/inch?

If the screen output, and especially if a printed copy at your place is of good quality, there must have been a problem with the provider...

You can point out to them that you were well beyond the recommended resolution and that with just a simple print you achieve a better result than their work.... They are obliged to redo the work for you for free.

Professional printers are a bit more precise than personal printers (thus amplifying defects), but the difference is really minimal!

For a quality print, your image must be at least 300 DPI (dots per inch).
Otherwise, the image will pixelate.

Hello,
I have an image that measures 14cm/10cm, with a resolution of 200 pixels/cm.

There must be something else...

An image of 14x10cm at 200 pixels/cm results in an image of 508 pixels/inch with a weight of about 20 MB in CMYK (less in RGB)

So it's not a question of resolution, but maybe the quality of the image at the source, or during the creation of the final file intended for the provider, there were incorrect saving settings...

Did you provide a PDF file or a JPG?

I provided a JPEG file that looks great on my screen and that I printed for testing. There was nothing to criticize. I think it’s the manufacturer who made a mistake in processing my order.

Thank you very much for your responses. I hope to receive a reprint or a refund.