If the arithmetic signs "+" and "/" and the numbers 2 and 4 are interchanged with one another, which one of the following equations becomes correct after the interchange?

Introduction / Context:
This question involves a simultaneous interchange of two operation signs and two numbers. Specifically, every plus sign and every division sign are swapped, and every 2 and 4 are swapped. We must apply these interchanges consistently to each candidate equation and then see which equation becomes true under normal arithmetic rules.

Given Data / Assumptions:

• We interchange "+" and "/".
• We interchange the digits 2 and 4 wherever they appear.
• After the interchange we evaluate the equations with usual precedence.
• The options to test are:
  • 4/2+3 = 6
  • 2+4/3 = 3
  • 4+2/6 = 1.5
  • 2+4/6 = 8

Concept / Approach:
For each option we rewrite the left hand side by swapping all instances of 2 with 4 and all instances of "+" with "/". Then we compute the new left side and compare it with the right side. Only one option will yield a true statement. It is important to apply both the sign swap and the number swap consistently within each expression.

Step-by-Step Solution:
Option (a): 4/2+3 = 6. Swap 2 and 4 to get 2/4+3, then swap "+" and "/" to get 2+4/3. The new equation is 2 + 4/3 = 6, whose left side is 2 + 1.333... = 3.333..., not 6, so it is false. Option (b): 2+4/3 = 3. Swap 2 and 4 to get 4+2/3, then swap signs to get 4/2+3. The new equation is 4/2 + 3 = 3, whose left side is 2 + 3 = 5, not 3, so it is false. Option (c): 4+2/6 = 1.5. Swap 2 and 4 to get 2+4/6, then swap signs to get 2/4+6. The new equation is 2/4 + 6 = 1.5, whose left side is 0.5 + 6 = 6.5, not 1.5, so it is false. Option (d): 2+4/6 = 8. Swap 2 and 4 to get 4+2/6, then swap signs to get 4/2+6. The new equation is 4/2 + 6 = 8. The left side is 2 + 6 = 8, so this equation is true.

Verification / Alternative check:
We can double check option (d) directly. After the full interchange, no other option gives an integer on the left side equal to its right side. Only option (d) gives exact equality, so it must be the unique correct choice.

Why Other Options Are Wrong:
Options (a), (b) and (c) each fail because their transformed left-hands do not match their right-hands. Their left sides evaluate to 3.333..., 5 and 6.5 respectively, while the right sides remain 6, 3 and 1.5. Hence they are clearly incorrect under the specified interchange rules.

Common Pitfalls:
Many candidates forget to swap both the signs and the numbers, or they swap them only once per equation instead of everywhere they appear. Another source of error is performing the swaps in the wrong order for individual symbols. The safest method is to first swap the digits, then swap the operators, and only after that evaluate the expression.

Final Answer:
Only the equation that becomes 4/2 + 6 = 8 after the specified interchanges is correct, so the correct choice is 2+4/6 = 8.