Well let's take a walk back into the realm of Mendelian Genetics!
The first problem is that you're looking at crossing a green egg layer with a blue egg layer. The male won't have laid eggs, so we can't be 100% on that, but let's say for the purposes of Explanation that we KNOW that our male carries the gene for blue eggs. Now we need to talk about how we EXPRESS that gene.
For Blue eggs, let's assume it's a DOMINANT trait. That means that You only need one parent to pass along the blue egg gene to get offspring that produce blue eggs. We'll use O to express this inheritance.
For Green eggs, let's assume this is recessive. This means that the duck must have the this green egg gene passed along from both mom and dad in order to produce green eggs. We'll use o to Express this inheritance.
Every parent has 2 genes, and each parent passes one of these to their offspring. So Mom has o/o while dad has O/o
In Mendelian genetics we chart this with a small grid
dad → O o
mom↓
o | O/o | o/o
o | O/o | o/o
This illustrates that the offspring has a 50% chance of laying blue eggs, and a 50% chance of laying green eggs.
Let's change dad to having both O genes though.
dad → O O
mom↓
o | O/o | O/o
o | O/o | O/o
Now none of the offspring would produce green eggs, but if those offspring were to mate with another bird that carried the recessive green gene, then we'd have a chart that looks like this:
dad → O o
mom↓
O | O/O | O/o
o | O/o | o/o
Now you that have the basics of what Mendel did with his pea plants in his studies in the 1800's I need to throw a wrench in here. The Blue and Green genes MAY NOT be as simple as a O and o as there are also white eggs! What if the Dominant trait (O) is for a white egg and the recessive is for blue, but there's another thing that influences how blue or how green? (this could be dietary, or this could be another gene expression.)
I don't have an answer for you, but I can provide you with a bit of background as to why the answer isn't exactly cut and dry.