Explanation:

Let's analyze each option by swapping numbers in the equation 9 + 4 ÷ 2 - 6 × 3 = 4 + 3 × 6 - 9 + 1 to find the correct balance:

- Option 1: Swap 6 and 3

- Modified: 9 + 4 ÷ 2 - 3 × 6 = 4 + 6 × 3 - 9 + 1

- Does not hold true.

- Option 2: Swap 4 and 9

- Modified: 9 + 9 ÷ 2 - 6 × 3 = 4 + 3 × 6 - 4 + 1

- Does not hold true.

- Option 3: Swap 4 and 2

- Modified: 9 + 2 ÷ 4 - 6 × 3 = 4 + 3 × 6 - 9 + 1

- Does not hold true.

- Option 4: Swap 6 and 4

- Modified: 9 + 6 ÷ 2 - 4 × 3 = 4 + 3 × 6 - 9 + 1

- Holds true.