How to write script to show next button after selecting 3 correct answers

Could be easy, but from the script you are showing (do not know the Preview button for Advanced actions?) the setup is rather complicated and you don't explain the setup. Why do the answers have to be greater than 0, is this about number answers? 

It can be very complicated (see Rod's answer) or very simple.... depending on what exactly you want.

Simple: if yoy only want to realize that Next button appears after having selected three correct answers, and you are fine with disabling the shape button with the answer (I suspect that you use shape buttons for the answers), it can be done with one counter variable and a two-decision action for each correct button. However without more details about what you want, impossible to explain.

You're going to need a more complex Conditional Action than this to achieve what you want.  You'll need a separate Decision Block for each possible permutation of answers.

You appear to have only three answers to choose from on the question (based on the fact that you have only three variables tracking what the learner selects). So, I am assuming that two of the three answers are correct and the third one is incorrect.  Is that so?

If I am correct, then you need to work out what should happen for each of these circumstances:

• The learner selects all threee answers.
• The learner selects the incorrect answer and none of the correct answers.
• The learner selects one of the correct answers as well as the incorrect answer. 
• The learner selects just one of the correct answers (but no incorrect one).
• The learner selects both of the correct answers.

Only if you know what should happen in each case will you then be able to design how the Conditional Action should work.