In this question, some equations are solved according to a specific pattern. Using the same pattern, where 3 X 4 X 5 = 435 and 4 X 3 X 2 = 342, what should be the value of 2 X 3 X 4?

Introduction / Context:
This coding question presents three numbers separated by X and equates them to a three digit result. The symbol X here does not represent ordinary multiplication but a special arrangement pattern. By examining the given examples, we must discover how the digits are rearranged and then apply that pattern to find the result corresponding to the third expression.

Given Data / Assumptions:

• 3 X 4 X 5 is coded as 435.
• 4 X 3 X 2 is coded as 342.
• We must find the code for 2 X 3 X 4.
• The X symbol indicates that the numbers are to be combined or rearranged, not multiplied.
• The pattern must be consistent in all given examples.

Concept / Approach:
When the coded answers are three digit numbers built from the same digits as the original three numbers, the most likely pattern is a rearrangement of the order of those numbers. The task becomes identifying which position each original number occupies in the result. Once we determine this mapping for one example, we must confirm it with the other example to ensure that the pattern is reliable.

Step-by-Step Solution:
Step 1: Look at 3 X 4 X 5 = 435. The three numbers are 3, 4 and 5, while the result 435 uses the digits 4, 3 and 5.Step 2: Observe that 435 can be seen as the middle number first (4), then the first number (3), followed by the last number (5). So the mapping seems to be (first, second, third) → (second, first, third).Step 3: Check this mapping with the second example 4 X 3 X 2 = 342. Using the same rule, the second number is 3, the first number is 4 and the third number is 2, giving 342, which matches the given result.Step 4: Since the mapping works for both examples, the rule is confirmed: the output is formed as second number, first number, third number.Step 5: Apply the rule to 2 X 3 X 4. Here the first number is 2, the second is 3 and the third is 4.Step 6: According to the rule, the result is second, first, third, which is 3, 2, 4, or 324.

Verification / Alternative check:
To verify, you can quickly encode 2 X 3 X 4 using any other plausible rearrangement, such as first, third, second or third, second, first. None of these patterns will give the previously established results for the earlier equations. Only the second, first, third pattern fits both the provided examples and the desired equation, confirming that 324 is the correct code.

Why Other Options Are Wrong:
The option 342 corresponds to the pattern second, third, first, which does not match the given example 3 X 4 X 5 = 435. The option 432 corresponds to third, second, first, again inconsistent with 435. The option 243 or 234 come from other arbitrary reorderings of 2, 3 and 4 that do not fit the verified rule. Only 324 respects the pattern discovered from the given equations.

Common Pitfalls:
One common mistake is to assume that multiplication is involved because of the symbol X and therefore spend time computing products or sums instead of noticing that only permutations of digits appear. Another mistake is to choose a rearrangement that works for one equation but not for the others. Always confirm the mapping across all examples before applying it to the target.

Final Answer:
Applying the same rearrangement pattern, the correct coded value of 2 X 3 X 4 is 324.