Step 1: Analyzing the pattern.
We need to find the relationship between the numbers within each box. Let's look at each box:
- Box 1: \( 3 + 6 = 9 \), and the bottom left number is \( 6 \), which could represent the difference between the two top numbers.
- Box 2: \( 1 + 6 = 7 \), and the bottom left number is \( 8 \), which seems to follow the same difference logic: \( 8 - 7 = 1 \).
- Box 3: \( 4 + 2 = 6 \), and the bottom left number is \( 7 \). Similarly, the difference is \( 7 - 6 = 1 \).
Step 2: Applying the pattern to Box 4.
In Box 4, \( 3 + 9 = 12 \), and the missing number must follow the same pattern. The difference between the sum \( 12 \) and the existing number \( 9 \) is \( 12 - 9 = 3 \). Therefore, the missing number is \( 7 \).
Final Answer:
\[
\boxed{7}
\]