The green background used for the number of answers given to a question shows the questions with an accepted answer.
When you don't see that green background, it means the question doesn't have an accepted answer.
This is true in any list of questions.
In your profile page, the part giving a summary of the posts you wrote still uses the green background to show the questions with an accepted answer, but (given the few space available) it shows the score of your questions.
So the first question shown in this screenshot has a score of 0, and you accepted an answer.
It can be a little confusing, but if you click on View more, you see exactly which questions have answers.
As you see, 0, 0, 1, 1, and 0 you see in the summary are the scores for the questions, and the green background is not used for questions without an answer.
For the summary of the answers you wrote, the green background shows which answers of yours have been accepted.