fin1570048093

I don't think this is possible. Some things you can do:
(a) use the announcement bar and mention customers can order a maximum of 4 free product samples at a time. I'm assuming you at least charge for shipping.
(b) include in each product description a note that customers can order only 4 free product samples at a time.
(c) in the Additional Information section during checkout, mention that only up to 4 product samples can be ordered at a time. Ask them to remove any other product samples over the limit.
(d) customize the confirmation email your customers receive to repeat the info: only 4 free products per order. If, after making it obvious on your site/store the 4-free-product-limit-per-order customers still put in more than 4 in their cart and check out, you can put in the confirmation email that only the first 4 free product samples will be sent to them.
There really is no way to set limits to the number of products customers are allowed to add to their carts, especially when it comes to free product samples.

Hi @fin1570048093
There are ways to achieve this with custom code, but the feasibility will depend on your site's template and the way it's been set up.  If you can provide me with a link to the site, I'll take a look and gain some context. For example, do you want to allow customers to select add just '1' of up to 4 samples, or 2 of two samples?
If the site isn't live, you'll also want to set a password in the visibility settings and share it with us. Without this, we won't be able to view the site.