Answer:
A brown eyed dad and a green eyed mom can have a blue eyed child because there are at least two eye color genes. Because of this, it is possible for both green and brown eyed parents to be carriers for blue eyes.
And as carriers, they each can pass down blue eye genes to their children. Let's go into a bit more detail about how all of this works. We'll also do Punnett squares for the two most likely possibilities in your case to figure out the chances of your parents having a blue eyed child.
As I said, eye color happens because of at least two separate genes. The first gene, OCA2, comes in two forms, brown (B) and blue (b). The second gene, called gey, comes in two forms, green (G) and blue (b). Here is a table that shows how these genes are thought to work together to create eye colors
Explanation: