If your order is shipped from the US to the EU, VAT will be applied if the order value (Printful product price) is less than 150 euro (approx. $183). To learn more about it, click here.
However, you may also be liable to charge VAT on orders going to EU member states. That means you would register as a VAT payer, charge customers in the EU, and remit VAT to the country in which you're registered.