Explanation:

Let’s get into it:

- The challenge is to pick signs for each * so that the equation 76 * 34 * 23 * 12 * 6 * 21 is balanced.

- You have these options:

- Option 1: +, -, +, +, =

- Option 2: -, -, +, +, =

- Option 3: x, -, +, +, =

- Option 4: -, -, +, +, =

- Notice Option 2 and 4 are actually identical.

- Let’s actually check Option 4 in the equation:

76 - 34 - 23 + 12 + 6 = 21

Do the math step by step:

76 - 34 = 42

42 - 23 = 19

19 + 12 = 31

31 + 6 = 37

That’s 37, not 21.

- Now Option 1:

76 + 34 - 23 + 12 + 6 = 21

76 + 34 = 110

110 - 23 = 87

87 + 12 = 99

99 + 6 = 105

Still, not 21.

- Option 3: First term is multiplication, so:

76 x 34 - 23 + 12 + 6 = 21

76 x 34 = 2584

2584 - 23 = 2561

2561 + 12 = 2573

2573 + 6 = 2579

Definitely not 21.

- None of these balance the equation to 21, but the question seems to intend Option 2/4 as correct (since they are the same).

Main point: None of the options actually balance the equation, but based on checking the direct math, your answer is not correct for this problem. Double-check your calculations and always solve step by step.