Given the instruction "interchange the signs + and − and also interchange the numbers 4 and 8 wherever they occur in an equation", which one of the following equations will become numerically correct after making all the stated interchanges?

Introduction / Context:
This problem involves a coded transformation applied to entire equations. We are told to interchange the plus and minus signs and also to interchange the numbers 4 and 8 wherever they appear. The aim is to decide which given equation will produce a true numerical statement once all of these interchanges are applied consistently to both sides of that equation.

Given Data / Assumptions:

• We must simultaneously replace every + with − and every − with +.
• We must simultaneously replace every 4 with 8 and every 8 with 4.
• The transformation is applied to the whole equation, including both left-hand and right-hand sides.
• We then evaluate the transformed equation with standard arithmetic rules.

Concept / Approach:
The correct strategy is to apply the substitution rules carefully to each candidate equation. After transforming the equation, we compute both sides and check whether the equality holds. The option for which the transformed left-hand side and right-hand side are equal is the correct answer. All other options will result in unequal sides after the transformation, so they will not represent valid equations.

Step-by-Step Solution:
Consider option B: 4 - 8 + 12 = 0.Apply sign changes: minus becomes plus and plus becomes minus, so 4 - 8 + 12 becomes 4 + 8 - 12, and the right-hand side 0 stays 0.Apply number changes: every 4 becomes 8 and every 8 becomes 4, so 4 + 8 - 12 becomes 8 + 4 - 12. The right-hand side is still 0.Evaluate the transformed left-hand side: 8 + 4 - 12 = 12 - 12 = 0, which matches the right-hand side.

Verification / Alternative check:
If we try option A: 4 + 8 - 12 = 12, the transformation eventually leads to 8 - 4 + 12 = 12 on the left and 12 stays 12 on the right, giving 16 ≠ 12.For option C: 8 + 4 - 12 = 24, after applying the rules, the left-hand side does not evaluate to the transformed right-hand side, so it is not a correct equation.The same inconsistency occurs with option D, so only option B produces a valid equality after all substitutions.

Why Other Options Are Wrong:
For each of A, C and D, at least one side of the equation changes in a way that alters the balance between left and right, so numerical equality is lost after transformation.Because the transformation systematically changes both signs and specific numbers, small changes in structure of the equation can easily make the equality fail.

Common Pitfalls:
A frequent mistake is to apply the transformations only to the left-hand side or only to the numbers, but not to both sides in a consistent way.Another error is to attempt mental substitution too quickly and misread 4 and 8 or the positions of plus and minus signs.

Final Answer:
The only equation that becomes correct after all specified interchanges is 4 - 8 + 12 = 0.