Hi,
I can see that you created two shipping methods. A free one and a 4.60€ one, and then you apparently created an auto loaded coupon with the same discount value as the value of the 4.60 shipping method, or something like that.
I can see that whatever the total amount of the cart is, both shipping methods are available to the user.
This tells me that either you didn't configure the "minimum price" and "maximum price" settings of your shipping methods, or you did, but you have their "include virtual products price" setting turned off and your products don't have a weight.
So please check all of this first.
Also, normally, you don't need a coupon. If there is only the free shipping method available for the current cart, it will be automatically selected, and then if you change something in the cart and only the other shipping method becomes available, it will be this other shipping method which will be selected automatically.
Either that, or you want to have only the 4.60 shipping method, and configure the auto loaded coupon to have its minimum order value to 40. That way, the coupon will be added or removed automatically based on the total amount, and the shipping method won't change.