Printful charges VAT for orders that are fulfilled in any Printful location with an end-address in an EU member state.
You need to collect VAT on orders that have an end-destination in the EU, regardless of where they're fulfilled.
This is the formula you should use to collect VAT:
(Your retail price + shipping + services - discounts)*VAT rate %. Services include embroidery file digitization.
The VAT rate percentage depends on the country that you're registered in and where the order is shipped. Take a look at each country's VAT rates here.