Let's solve the inequality step by step. The given inequality is:

$-8 > 11 + x$

Step 1: Isolate the variable $x$

Subtract 11 from both sides to move the constant to the left side:

$-8 - 11 > x$

This simplifies to:

$-19 > x$

Step 2: Rewrite the inequality

We can rewrite this as:

$x < -19$

Thus, the number that belongs in the green box is -19.

Let me know if you need more details or have any questions! Here are five related questions you might want to explore:

1. What happens if we multiply or divide both sides of an inequality by a negative number?
2. How do inequalities change when solving for absolute values?
3. Can you graph the solution for this inequality on a number line?
4. What is the difference between solving equations and inequalities?
5. How do we solve compound inequalities that involve "and" or "or" conditions?

Tip: When solving inequalities, if you multiply or divide by a negative number, you must reverse the inequality sign.