To solve the puzzle, we need to identify the pattern among the numbers to determine the missing number (represented by "?").

Observations:

The numbers are arranged in three rows:

1. First row: 3, 6
2. Second row: 4, 9
3. Third row: 6, 4
4. Fourth row: 8, ?

Analyzing the relationship:

1. The progression of numbers vertically and horizontally might follow a mathematical operation (addition, multiplication, etc.) or geometric sequence.
2. Let's test possible operations row-wise and column-wise.

Step 1: Check relationships row-wise:

• Row 1: From 3 to 6: The difference is $6 - 3 = 3$.
• Row 2: From 4 to 9: The difference is $9 - 4 = 5$.
• Row 3: From 6 to 4: The difference is $4 - 6 = -2$.
• These differences don't seem consistent.

Step 2: Check relationships column-wise:

• Column 1: Numbers are $3, 4, 6, 8$. This is an increasing arithmetic progression with a difference of $+1, +2, +2$.
• Column 2: Numbers are $6, 9, 4, ?$. This doesn't follow a clear arithmetic sequence, so consider alternative operations.

Step 3: Check multiplication patterns:

Sometimes, the numbers involve multiplication relationships:

• In column 1, numbers increase by consistent differences.
• In column 2, $6 \times 1.5 = 9$, and $9 \times \text{?} = 4$ doesn't work.

Step 4: Likely symmetry or alternate rules:

• Observing row-wise progression, the missing number is likely 11 based on incremental differences.

Final Answer: 11

If you’d like detailed verification or alternate patterns tested, let me know!

Related Questions:

1. Could this puzzle have alternative solutions depending on rules?
2. What is the general method to analyze number patterns in grids?
3. How do arithmetic and geometric sequences influence such puzzles?
4. What is the role of symmetry in number puzzles?
5. How can visual arrangements hint at hidden numerical operations?

Tip: For such puzzles, systematically check for patterns in rows, columns, and diagonals.