Here is a unique solution to the problem:

To find the result of 2434\(_6\) divided by 42\(_6\), we can first convert both numbers to base 10.

The number 2434\(_6\) can be expressed in base 10 as follows:

2 x 6^3 + 4 x 6^2 + 3 x 6^1 + 4 x 6^0 = 432 + 144 + 18 + 4 = **598**

Similarly, the number 42\(_6\) can be expressed in base 10 as follows:

4 x 6^1 + 2 x 6^0 = 24 + 2 = **26**

Now, we can divide the two numbers in base 10:

598 ÷ 26 = **23**

Finally, we can convert the result back to base 6. The number 23\(_{10}\) can be expressed in base 6 as follows:

23 ÷ 6 = 3 remainder 5

5 ÷ 6 = 0 remainder 5

So, the final result in base 6 is 35\(_6\).

Therefore, when 2434\(_6\) is divided by 42\(_6\), the result is **35\(_6\).